problem-solver

problem-solver

Purpose

Structured reasoning utility for problems that resist straightforward analysis. Receives a problem statement, detects cognitive biases, selects the appropriate analytical framework, applies it step-by-step with evidence, and returns ranked solutions with a communication structure. Stateless — no memory between calls.

Inspired by McKinsey problem-solving methodology and cognitive science research on decision-making errors.

Calls (outbound)

None — pure L3 reasoning utility.

Called By (inbound)

• debug (L2): complex bugs that resist standard debugging
• brainstorm (L2): structured frameworks for creative exploration
• plan (L2): complex architecture decisions with many trade-offs
• ba (L2): requirement analysis when scope is ambiguous

Execution

Input

problem: string         — clear statement of the problem to analyze
context: string         — (optional) relevant background, constraints, symptoms observed
goal: string            — (optional) desired outcome or success criteria
mode: string            — (optional) "analyze" | "decide" | "decompose" | "communicate"

Step 1 — Receive and Classify

Read the problem and context inputs. Restate the problem in one sentence to confirm understanding.

Classify the problem type:

Type	Signal Words	Primary Approach
Root cause / diagnostic	"why", "broken", "failing", "declining"	5 Whys, Fishbone, Root Cause
Decision / choice	"should I", "choose", "compare", "vs"	Decision Frameworks (Step 3b)
Decomposition	"break down", "understand", "structure"	Decomposition Methods (Step 3c)
Creative / stuck	"stuck", "no ideas", "exhausted options"	SCAMPER, Collision-Zone, Inversion
Architecture / scale	"design", "architecture", "will it scale"	First Principles, Scale Game

Step 1.5 — Domain Classification (Cynefin)

Before selecting a framework, classify the problem's complexity domain. This determines HOW MUCH analysis is warranted and WHICH class of frameworks applies.

Domain	Signal	Framework Class	Analysis Depth
Clear (obvious)	Best practice exists, cause-effect obvious, "just do X"	Direct action — no framework needed	Minimal — act immediately
Complicated (expert analysis)	Cause-effect discoverable through analysis, multiple right answers exist	Analytical frameworks (5 Whys, Fishbone, SWOT, Weighted Matrix)	Moderate — structured analysis
Complex (emergent)	Cause-effect only visible in retrospect, no right answer — only better probes	Probe-sense-respond (Pre-Mortem, Systems Map, Sensitivity Analysis, PESTLE)	Deep — experiment and iterate
Chaotic (crisis)	No cause-effect, need to stabilize first	Act-sense-respond — triage, then analyze	Immediate — stabilize before analyzing
Confused (don't know which domain)	Can't classify → decompose until sub-problems land in a known domain	Decomposition first (Issue Tree, MECE) → re-classify each branch	Meta — decompose then classify

Output: State the domain and justify in one sentence. If Confused, decompose before proceeding.

Why this matters: Applying Complicated-domain tools (deep analysis) to a Clear problem wastes effort. Applying Clear-domain tools ("just do X") to a Complex problem creates false confidence. Match the tool to the terrain.

Step 2 — Bias Check (ALWAYS RUN)

NEVER skip bias detection. Every problem has biases — explicitly address them. This is the #1 value-add from structured reasoning. Without it, solutions are just dressed-up gut feelings.

Scan the problem statement and context for bias indicators. Check the top 6 most dangerous biases:

Bias	Detection Question	Debiasing Strategy
Confirmation Bias	Have we actively sought evidence AGAINST our preferred option? Are we explaining away contradictory data?	Assign devil's advocate. Explicitly seek disconfirming evidence. Require equal analysis of all options.
Anchoring Effect	Would our evaluation change if we saw options in a different order? Is the first number/proposal dominating?	Generate evaluation criteria BEFORE seeing options. Score independently before group discussion.
Sunk Cost Fallacy	If we were starting fresh today with zero prior investment, would we still choose this? Are we justifying by pointing to past spend?	Evaluate each option as if starting fresh (zero-based). Separate past investment from forward-looking decision.
Status Quo Bias	Are we holding the current state to the SAME standard as alternatives? Would we actively choose the status quo if starting from scratch?	Explicitly include status quo as an option evaluated with same rigor. Calculate the cost of inaction.
Overconfidence	What is our confidence level, and what is it based on? Have we been right about similar predictions before?	Use pre-mortem to stress-test. Track calibration. Seek outside perspectives.
Planning Fallacy	Are our estimates based on best-case assumptions? Have similar projects in the past taken longer or cost more?	Use reference class forecasting — compare to actual outcomes of similar past efforts rather than bottom-up estimates.

Additional biases to check when relevant:

• Framing Effect: Would our preference change if framed as a gain vs. a loss?
• Availability Heuristic: Are we basing estimates on vivid anecdotes rather than systematic data?
• Groupthink: Has anyone expressed strong disagreement? Are we reaching consensus suspiciously fast?
• Loss Aversion: Are we avoiding an option primarily because of what we might lose, rather than evaluating the full picture?
• Survivorship Bias: Are we only looking at successful cases? Who tried this approach and failed?
• Recency Bias: Are we extrapolating from the last few data points instead of looking at 5-10 years of data?

Steel Manning (apply when evaluating competing options): Before dismissing any option, construct the STRONGEST possible version of the argument for it. If you can't articulate why a smart, informed person would choose it, you haven't understood it yet. Steel Manning prevents strawman dismissals and forces genuine evaluation.

Output: List 2-3 biases most likely to affect THIS specific problem, with their debiasing strategy. If comparing options, include a steel-manned case for the option you're least inclined toward. Weave these warnings into the analysis.

Step 3a — Select Analytical Framework

Choose the framework based on what is unknown about the problem:

Situation	Framework
Root cause unknown — symptoms clear	5 Whys
Multiple potential causes from different domains	Fishbone (Ishikawa)
Standard assumptions need challenging	First Principles
Creative options needed for known problem	SCAMPER
Must prioritize among known solutions	Impact Matrix
Conventional approaches exhausted, need breakthrough	Collision-Zone Thinking
Feeling forced into "the only way"	Inversion Exercise
Same pattern appearing in 3+ places	Meta-Pattern Recognition
Complexity spiraling, growing special cases	Simplification Cascades
Unsure if approach survives production scale	Scale Game
High-stakes irreversible decision — need to find blind spots	Pre-Mortem
Need to determine how much analysis effort is warranted	Reversibility Filter
Quantifiable outcomes with estimable probabilities	Expected Value Calculation
Key assumptions uncertain, need to know what flips the decision	Sensitivity Analysis
Need holistic internal + external assessment of a project/product/strategy	SWOT Analysis
Decision depends on macro-environment factors beyond your control	PESTLE Analysis
Competitive landscape unclear, need to assess market position	Porter's Five Forces
Need a rough estimate with very little data	Fermi Estimation
Problem involves ethical trade-offs or stakeholder harm	Ethical Reasoning (→ Step 5.5)

State which framework was selected and why.

SWOT Analysis (holistic assessment):

1. Strengths: Internal advantages — what do we do well? What assets do we have?
2. Weaknesses: Internal disadvantages — where are we vulnerable? What do we lack?
3. Opportunities: External factors we could exploit — trends, market gaps, timing
4. Threats: External factors that could harm us — competitors, regulation, tech shifts
5. Cross-reference: How can Strengths exploit Opportunities? How do Weaknesses amplify Threats?
6. Prioritize: Which quadrant demands immediate action?

PESTLE Analysis (macro-environment scan): When the problem is influenced by forces beyond the project/org:

Factor	Key Questions
Political	Government policy, regulation changes, political stability, trade restrictions?
Economic	Market conditions, inflation, exchange rates, funding climate, customer spending?
Social	Demographics, cultural trends, user behavior shifts, workforce expectations?
Technological	New tech, disruption risk, automation, platform shifts, AI impact?
Legal	Compliance requirements, IP, data privacy (GDPR/CCPA), licensing, liability?
Environmental	Sustainability expectations, carbon footprint, resource scarcity, ESG pressure?

For each factor: rate impact (high/medium/low) and timeline (imminent/near-term/long-term). Focus analysis on high-impact factors only.

Porter's Five Forces (competitive position):

1. Threat of New Entrants: How easy is it for competitors to enter? (barriers: capital, tech, brand, network effects)
2. Bargaining Power of Suppliers: How much leverage do your dependencies have? (few suppliers = high power)
3. Bargaining Power of Buyers: Can customers easily switch? (low switching cost = high power)
4. Threat of Substitutes: What alternatives exist outside your direct market?
5. Competitive Rivalry: How intense is competition? (many similar players = high rivalry) Rate each force: strong / moderate / weak. Strongest forces dictate strategy.

Fermi Estimation (order-of-magnitude reasoning): When data is scarce but a rough estimate is needed:

1. Break the unknown into estimable sub-components
2. Estimate each component using common knowledge or reference classes
3. Multiply/combine to get the overall estimate
4. Sanity-check: does the result pass the smell test? Off by 10x?
5. State confidence range: "between X and Y, best estimate Z" Goal: be within an order of magnitude (10x), not precise. Useful for sizing markets, estimating effort, or validating claims.

Step 3b — Decision Frameworks (when mode = "decide")

When the problem is a decision/choice, use these specialized frameworks:

Reversibility Filter (always apply first):

• Is this a one-way door (irreversible) or two-way door (reversible)?
• Two-way door → decide quickly, set review date, iterate
• One-way door → invest in thorough analysis, use other frameworks
• Proportional effort: analysis depth should match reversibility

Weighted Criteria Matrix (multi-option comparison):

1. List all options
2. Define 3-5 evaluation criteria (max 5 — more causes choice overload)
3. Assign weights (must sum to 100)
4. Score each option 1-5 on each criterion
5. Calculate weighted scores
6. Run sensitivity: which weight changes would flip the decision?

Pros-Cons-Fixes (binary or few-option, quick):

1. List pros and cons for each option
2. For each con: can it be fixed, mitigated, or is it permanent?
3. Re-evaluate with fixable cons addressed
4. Decide based on remaining permanent trade-offs

Pre-Mortem (high-stakes, irreversible):

1. Assume the decision has already failed catastrophically (12 months later)
2. List what went wrong (work backward)
3. Categorize by likelihood and severity
4. Develop mitigation plans for high-risk failures

Expected Value (quantifiable outcomes):

1. List possible outcomes for each option
2. Estimate probability of each
3. Estimate value (monetary or utility) of each
4. Calculate EV = Σ(probability × value)
5. Choose highest EV adjusted for risk tolerance

Regret Minimization (life-scale or career-scale decisions):

1. Project yourself to age 80 (or 10 years from now)
2. Ask: "Will I regret NOT trying this?" — regret of inaction vs. regret of action
3. Regret of inaction (missed opportunity) typically outweighs regret of action (failed attempt)
4. Use when: the decision is personally significant, emotionally charged, or involves a window of opportunity that won't return
5. Not suitable for: purely analytical/technical decisions — use Expected Value instead

Step 3c — Decomposition Methods (when mode = "decompose")

When the problem needs structuring before analysis:

Method	When to Use	Pattern
Issue Tree	Don't have a hypothesis yet, exploring	Root Question → Sub-questions (why/what) → deeper
Hypothesis Tree	Have domain expertise, need speed	Hypothesis → Conditions that must be true → Evidence needed
Profitability Tree	Business performance problem	Profit → Revenue (Price × Volume) → Costs (Fixed + Variable)
Process Flow	Operational/efficiency problem	Step 1 → Step 2 → ... → find bottleneck
Systems Map	Complex with feedback loops	Variables → causal links (+/-) → reinforcing/balancing loops
Customer Journey	User/customer problem	Awareness → Consideration → Purchase → Experience → Retention

All decompositions MUST pass the MECE test:

• ME (Mutually Exclusive): branches don't overlap
• CE (Collectively Exhaustive): branches cover all possibilities

Step 4 — Apply Framework

Execute the selected framework with discipline. For each framework, follow the steps defined in Step 3a/3b/3c.

At each step, apply the bias debiasing strategies identified in Step 2.

Step 5 — Apply Mental Models

Cross-check the framework output against relevant mental models:

Model	Core Question	When It Helps
Second-Order Thinking	"And then what?" — consequences of consequences	Decisions with delayed effects
Bayesian Updating	How should we update our beliefs given this new evidence?	When new data arrives during analysis
Margin of Safety	What buffer do we need for things going wrong?	Planning timelines, budgets, capacity
Opportunity Cost	What's the best alternative we're giving up?	Resource allocation, project prioritization
Occam's Razor	Among competing explanations, prefer the simplest	Multiple possible root causes
Leverage Points	Where does small effort produce large effect?	System redesign, process improvement
Hanlon's Razor	Never attribute to malice what can be explained by incompetence or misaligned incentives	Organizational problems, team conflicts
Regression to the Mean	Is this extreme result likely to revert to average?	After exceptional performance (good or bad)
Dialectical Thinking	Thesis + Antithesis → can we synthesize a higher-order solution?	Two opposing valid positions, binary choice feels forced
Fermi Estimation	Can we get a rough order-of-magnitude estimate to sanity-check?	Claims, estimates, or projections that feel off

Apply 1-2 most relevant models. State which and why.

Step 5.5 — Ethical Dimension Check (when applicable)

Run this check when the problem involves: user data, automation replacing human judgment, resource allocation affecting people, public-facing decisions, or stakeholder trade-offs.

Lens	Core Question
Harm	Who could be harmed by each option? How severe? How reversible?
Fairness	Does this option disadvantage any group disproportionately?
Transparency	Would we be comfortable if our reasoning was public?
Autonomy	Does this preserve user choice, or does it decide for them?
Long-term trust	Will this erode trust with users/team/community over time?

This is NOT a gate — it produces warnings, not blocks. If an ethical concern is identified, note it alongside the solution in Step 6 so the decision-maker can weigh it.

Skip this step for purely technical problems with no stakeholder impact (e.g., "which sorting algorithm").

Step 6 — Generate Solutions

From the framework output, derive 2-3 actionable solutions. For each:

• Describe what to do concretely
• Estimate impact: high / medium / low
• Estimate effort: high / medium / low
• State any preconditions or risks
• Note which biases might affect evaluation of this solution

Rank solutions by impact/effort ratio.

Step 7 — Select Communication Structure

Choose how to present the analysis based on audience:

Audience	Pattern	Format
Executive / senior	Pyramid Principle	Lead with recommendation → support with 3 arguments → evidence
Mixed / unfamiliar	SCR	Situation (context) → Complication (tension) → Resolution (recommendation)
Technical / peers	Day-1 Answer	State best hypothesis → list evidence for/against → confidence level
Quick update	BLUF	Bottom Line Up Front → background → details → action required

Structure the output report using the selected pattern.

Constraints

• MUST run domain classification (Step 1.5) — match analysis depth to problem complexity
• MUST run bias check (Step 2) for EVERY problem — the bias layer IS the differentiator
• MUST steel-man the least-favored option when comparing alternatives
• Never skip the framework — the structure is the value
• Use Sonnet, not Haiku — reasoning depth matters
• If problem is underspecified, state assumptions explicitly before proceeding
• Do not produce more than 3 recommended solutions — prioritize quality over quantity
• Max 5 evaluation criteria in Weighted Matrix — more causes choice overload
• Decompositions MUST pass MECE test — no overlapping or missing branches

Output Format

## Analysis: [Problem Statement]
- **Type**: [root cause / decision / decomposition / creative / architecture]
- **Domain**: [Clear / Complicated / Complex / Chaotic / Confused] — [one-line justification]
- **Framework**: [chosen framework and reason]
- **Confidence**: high | medium | low

### Bias Warnings
- ⚠️ [Bias 1]: [how it might affect this analysis] → [debiasing action taken]
- ⚠️ [Bias 2]: [how it might affect this analysis] → [debiasing action taken]

### Reasoning Chain
1. [step with evidence or reasoning]
2. [step with evidence or reasoning]
3. [step with evidence or reasoning]
...

### Mental Model Cross-Check
- [Model applied]: [insight gained]

### Root Cause / Core Finding
[what the framework reveals as the fundamental issue or conclusion]

### Recommended Solutions (ranked)
1. **[Solution Name]** — Impact: high/medium/low | Effort: high/medium/low
   [concrete description of what to do]
   ⚠️ Bias risk: [which bias might make us over/under-value this]
2. **[Solution Name]** — Impact: high/medium/low | Effort: high/medium/low
   [concrete description of what to do]
3. **[Solution Name]** — Impact: high/medium/low | Effort: high/medium/low
   [concrete description of what to do]

### Next Action
[single most important immediate step]

Sharp Edges

Failure Mode	Severity	Mitigation
Skipping bias check and jumping to framework	CRITICAL	HARD-GATE: Step 2 is mandatory — biases ARE the value-add
Skipping the framework and jumping to solutions	CRITICAL	Solutions without structured analysis are guesses
Proceeding with underspecified problem	HIGH	Step 1: restate in one sentence — if ambiguous, state interpretation
Producing more than 3 solutions	MEDIUM	Max 3 ranked — prioritize quality over quantity
Framework mismatch (5 Whys for a creative problem)	MEDIUM	Use selection table — match framework to "what is unknown"
Weighted Matrix with > 5 criteria	MEDIUM	Choice overload — max 5 criteria, focus on what matters
Pre-Mortem without debiasing strategies	MEDIUM	Pre-Mortem reveals risks — MUST include mitigation plans
Decomposition failing MECE test	HIGH	Every branch must be ME (no overlap) and CE (no gaps)
Ignoring second-order effects in recommendations	MEDIUM	Apply Second-Order Thinking: "and then what?"
Presenting analysis without communication structure	LOW	Step 7: match output pattern to audience
Using Complicated-domain tools on a Complex problem	HIGH	Step 1.5 Cynefin: Complex → probe-sense-respond, not analyze-plan-execute
Strawmanning the least-favored option	MEDIUM	Steel Manning: build strongest case for option you dislike before dismissing
Running full PESTLE on a purely technical problem	LOW	PESTLE is for macro-environment — skip for algorithm/implementation choices
Skipping ethics check on user-facing decisions	MEDIUM	Step 5.5: lightweight check — warnings not gates, but don't skip for stakeholder-affecting decisions

Done When

• Problem restated in one sentence (understanding confirmed)
• Domain classified (Cynefin: Clear / Complicated / Complex / Chaotic / Confused)
• Bias check completed — 2-3 biases identified with debiasing strategies
• Framework selected with explicit reason stated
• Framework applied step-by-step with evidence at each step
• Mental models cross-checked (1-2 relevant models applied)
• 2-3 solutions ranked by impact/effort ratio with bias risk noted
• Next Action identified (single most important immediate step)
• Analysis Report emitted with communication structure

Cost Profile

~500-1500 tokens input, ~800-1500 tokens output. Sonnet for reasoning quality. Opus recommended for high-stakes irreversible decisions.