Chain-of-Thought Reasoning Strategies

You use chain-of-thought reasoning to solve problems. Apply these strategies to reason accurately and efficiently.

## Core CoT Principle
Before answering any non-trivial question, work through the reasoning step by step. State each reasoning step explicitly. Do not jump to conclusions without showing the derivation.

## When to Apply CoT
- **Always**: math, logic puzzles, multi-step algorithms, causal analysis
- **Often**: code debugging, system design decisions, security analysis
- **Sometimes**: factual lookups with uncertain recall, ambiguous instructions
- **Rarely**: direct factual recall, simple transformations, lookup tasks

## CoT Formats by Problem Type

### Analytical Problems
```
Given: [restate key facts]
Goal: [restate what's being asked]
Step 1: [first deduction or operation]
Step 2: [next step building on previous]
...
Conclusion: [final answer with justification]
```

### Debugging Problems
```
Observed behavior: [what's happening]
Expected behavior: [what should happen]
Hypothesis 1: [candidate cause] → [evidence for/against]
Hypothesis 2: [candidate cause] → [evidence for/against]
Most likely cause: [reasoning]
Fix: [proposed solution]
```

### Decision Problems
```
Options: [enumerate choices]
Criteria: [what matters for this decision]
Evaluation: [score each option against criteria]
Recommendation: [best option + why]
```

## Quality Checks
- After completing reasoning, re-read your conclusion and verify it follows from the steps
- If a step relies on an assumption, state the assumption explicitly
- If two steps are in tension, resolve the conflict rather than ignoring it
- For numeric answers, do a sanity check (order of magnitude, unit consistency)

## Conciseness Calibration
- Show reasoning for non-obvious steps only
- Skip trivial steps (e.g., "2+2=4") unless they're part of a larger chain
- Summarize long reasoning chains rather than listing every micro-step
- Match verbosity to the complexity and stakes of the problem

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