Reasoning Frameworks

• Scope: Reasoning, problem decomposition, and analysis techniques
• Load if: Planning implementation, evaluating arguments, estimating scope, decomposing tasks
• Prerequisites: @smith-guidance/SKILL.md

Foundation: Based on OODA Loop's Orient phase (Boyd) - the "cognitive engine" that drives decision-making through mental models, prior experience, and analysis/synthesis.

When to use: Problem framing, solution design, risk assessment, logical validation.

MECE relationship:

• smith-analysis (this file) - Constructive thinking (how to reason)
• @smith-clarity/SKILL.md - Defensive thinking (what to avoid)
• @smith-validation/SKILL.md - Proving/testing (verifying correctness)

Reasoning Patterns

Deductive Reasoning

General principles to specific conclusions (logically certain):

Pattern: If all A are B, and C is A, then C is B.

1. Start with general premise (known to be true)
2. Apply to specific case
3. Derive guaranteed conclusion

Inductive Reasoning

Specific observations to general patterns (probabilistic):

Pattern: Observed A1, A2, A3... all have property B. Therefore all A probably have B.

1. Gather specific observations
2. Identify patterns
3. Form general hypothesis (may be wrong)

Caution: Inductive conclusions can be wrong.

Abductive Reasoning

Best explanation from incomplete observations (inference to best explanation):

Pattern: B is observed. A would explain B. Therefore A is probably true.

1. Observe surprising/unexpected result
2. Generate candidate explanations
3. Select most plausible explanation
4. Test to confirm or falsify

Extended Thinking Guidance

Modern LLMs have built-in extended thinking for complex problem-solving.

When to use: Complex architectural decisions, multi-step refactoring, security analysis, performance optimization.

• NEVER use "think step-by-step" prompts (counterproductive for models with built-in reasoning)
• NEVER ask for visible reasoning steps (defeats efficiency purpose)
• NEVER use for simple, straightforward tasks
• NEVER provide explicit reasoning instructions (focus on outcome specification, not process)

Problem Decomposition

First Principles Thinking

Break down to fundamentals, reason up:

1. Identify assumptions - What do we take for granted?
2. Decompose - What are the fundamental truths?
3. Reconstruct - Build solution from first principles only

Polya's 4-Step Method

Universally applicable problem-solving:

1. Understand the problem

   • What is the unknown? What are the data? What is the condition?
   • Can you restate in your own words?

2. Devise a plan

   • Have you seen this before? Know a related problem?
   • Can you solve a simpler problem first?

3. Carry out the plan

   • Execute each step, check as you go
   • Can you prove each step correct?

4. Look back

   • Can you check the result differently?
   • Can you use this for other problems?

Estimation

Fermi Estimation

Order-of-magnitude approximation with limited data:

1. Break complex question into simpler sub-questions
2. Make reasonable assumptions for each part
3. Combine estimates (multiply/add as appropriate)
4. Sanity check: Is result reasonable?

Constraint Thinking

TOC Five Focusing Steps

Systematic bottleneck elimination (Goldratt):

1. Identify - Find the constraint limiting throughput
2. Exploit - Maximize constraint output without additional investment
3. Subordinate - Align everything else to support the constraint
4. Elevate - Increase constraint capacity if still limiting
5. Repeat - Find the new constraint (it will shift)

Three-Point Estimation (PERT)

Handle uncertainty with optimistic, likely, pessimistic:

• O: Best case (everything goes right)
• M: Most likely (typical scenario)
• P: Pessimistic (realistic worst case)
• Expected: (O + 4M + P) / 6

Current Reality Tree (CRT)

Trace symptoms to root cause:

1. List Undesirable Effects (UDEs) - symptoms observed
2. Connect with "if...then" cause-effect logic
3. Trace backward to find common root cause
4. Validate: Does root cause explain ALL symptoms?

Risk Assessment

Pre-Mortem Analysis

Before implementation, imagine failure has occurred:

1. Assume failure - "The project failed. Why?"
2. Generate causes - List reasons independently
3. Categorize - Group failure modes
4. Mitigate - Address highest-risk items in plan

Increases problem identification by 30%.

Inversion Thinking

Think backward to avoid failure:

• Instead of "How do I succeed?" ask "How could I fail?"
• Instead of "How to make this fast?" ask "What would make this slow?"
• Avoid stupidity rather than seeking brilliance

Comprehensive Review

Six Thinking Hats

Ensure coverage by examining from 6 perspectives:

• White (Facts): What data/evidence do we have?
• Red (Intuition): What does gut feeling say? Any concerns?
• Black (Caution): What could go wrong? What are the risks?
• Yellow (Optimism): What are the benefits? Best case?
• Green (Creativity): What alternatives exist? New approaches?
• Blue (Process): Are we on track? What's the next step?

ACTION (Recency Zone)

When reasoning or planning:

1. Use First Principles to break down complex problems
2. Apply Polya's 4-Step Method for systematic problem-solving
3. Use Pre-Mortem Analysis before implementation
4. Apply Six Thinking Hats for comprehensive review

• @smith-guidance/SKILL.md - Anti-sycophancy, HHH framework, exploration workflow
• @smith-clarity/SKILL.md - Cognitive guards, logic fallacies
• @smith-validation/SKILL.md - Hypothesis testing, debugging