---
name: complex-reasoning
description: Multi-step reasoning patterns and frameworks for systematic problem solving. Activate for Chain-of-Thought, Tree-of-Thought, hypothesis-driven debugging, and structured analytical approaches that leverage extended thinking.
allowed-tools:
  - Bash
  - Read
  - Write
  - Edit
  - Glob
  - Grep
  - Task
  - WebFetch
dependencies:
  - extended-thinking
triggers:
  - chain of thought
  - tree of thought
  - step by step
  - reasoning
  - systematic
  - hypothesis
  - debug complex
  - break down
  - analyze systematically
  - multi-step
---

# Complex Reasoning Skill

Structured reasoning frameworks for systematic problem solving, leveraging extended thinking capabilities for deep analysis.

## When to Use

- **Debugging complex issues** with multiple potential causes
- **Architecture decisions** requiring trade-off analysis
- **Root cause analysis** for production incidents
- **Performance optimization** with multiple variables
- **Security vulnerability assessment**
- **Code refactoring** with many dependencies

## Reasoning Frameworks

### Chain-of-Thought (CoT)

Linear step-by-step reasoning for sequential problems.

```markdown
## Chain-of-Thought Analysis

**Problem**: [State the problem clearly]

**Step 1: Understand the Context**
- What do we know?
- What are the constraints?
- What is the expected outcome?

**Step 2: Identify Key Components**
- Component A: [description]
- Component B: [description]
- Interactions: [how they relate]

**Step 3: Analyze Each Component**
- Component A analysis...
- Component B analysis...

**Step 4: Synthesize Findings**
- Key insight 1
- Key insight 2

**Step 5: Formulate Solution**
- Recommended approach
- Rationale
- Trade-offs

**Conclusion**: [Final recommendation with confidence level]
```

### Tree-of-Thought (ToT)

Branching exploration for problems with multiple solution paths.

```markdown
## Tree-of-Thought Exploration

**Root Problem**: [Problem statement]

### Branch 1: Approach A
├── Pros: [List advantages]
├── Cons: [List disadvantages]
├── Feasibility: [High/Medium/Low]
├── Sub-branch 1.1: [Variation]
│   └── Outcome: [Expected result]
└── Sub-branch 1.2: [Variation]
    └── Outcome: [Expected result]

### Branch 2: Approach B
├── Pros: [List advantages]
├── Cons: [List disadvantages]
├── Feasibility: [High/Medium/Low]
└── Sub-branches: [...]

### Branch 3: Approach C
├── Pros: [...]
├── Cons: [...]
└── Feasibility: [...]

### Evaluation Matrix
| Approach | Feasibility | Impact | Risk | Score |
|----------|-------------|--------|------|-------|
| A        | High        | Medium | Low  | 8/10  |
| B        | Medium      | High   | Med  | 7/10  |
| C        | Low         | High   | High | 5/10  |

**Selected Path**: Branch [X] because [reasoning]
```

### MECE Framework

Mutually Exclusive, Collectively Exhaustive analysis.

```markdown
## MECE Analysis

**Problem Space**: [Define the complete problem]

### Category 1: [Mutually exclusive category]
- Sub-element 1.1
- Sub-element 1.2
- Sub-element 1.3

### Category 2: [Mutually exclusive category]
- Sub-element 2.1
- Sub-element 2.2

### Category 3: [Mutually exclusive category]
- Sub-element 3.1
- Sub-element 3.2
- Sub-element 3.3

**Completeness Check**:
- [ ] Categories are mutually exclusive (no overlap)
- [ ] Categories are collectively exhaustive (cover all cases)
- [ ] Each sub-element belongs to exactly one category

**Priority Matrix**:
| Category | Urgency | Impact | Action |
|----------|---------|--------|--------|
| 1        | High    | High   | Now    |
| 2        | Medium  | High   | Next   |
| 3        | Low     | Medium | Later  |
```

### Hypothesis-Driven Debugging

Systematic approach to debugging complex issues.

```markdown
## Hypothesis-Driven Debug Session

**Symptom**: [Observed behavior]
**Expected**: [What should happen]
**Environment**: [Relevant context]

### Hypothesis 1: [Most likely cause]
**Evidence For**:
- [Supporting observation 1]
- [Supporting observation 2]

**Evidence Against**:
- [Contradicting observation]

**Test**: [How to validate]
**Result**: [Confirmed/Refuted]

### Hypothesis 2: [Second most likely]
**Evidence For**:
- [...]

**Evidence Against**:
- [...]

**Test**: [...]
**Result**: [...]

### Root Cause Identified
**Cause**: [Confirmed root cause]
**Evidence Chain**: [How we proved it]
**Fix**: [Remediation steps]
**Prevention**: [How to prevent recurrence]
```

## Code Analysis Patterns

### Dependency Analysis

```markdown
## Dependency Analysis: [Component Name]

### Direct Dependencies
| Dependency | Version | Purpose | Risk Level |
|------------|---------|---------|------------|
| dep-a      | 2.3.1   | Auth    | Low        |
| dep-b      | 1.0.0   | Data    | Medium     |

### Transitive Dependencies
- Total: [N] packages
- Security vulnerabilities: [N]
- Outdated: [N]

### Dependency Graph
```
[component]
├── dep-a
│   ├── sub-dep-1
│   └── sub-dep-2
└── dep-b
    └── sub-dep-3
```

### Risk Assessment
1. **High Risk**: [Dependencies with known issues]
2. **Medium Risk**: [Outdated or unmaintained]
3. **Low Risk**: [Stable, well-maintained]

### Recommendations
1. [Action item 1]
2. [Action item 2]
```

### Impact Analysis

```markdown
## Impact Analysis: [Proposed Change]

### Affected Components
| Component | Impact Type | Severity | Test Required |
|-----------|-------------|----------|---------------|
| Service A | Direct      | High     | Yes           |
| Service B | Indirect    | Medium   | Yes           |
| Client C  | Downstream  | Low      | Optional      |

### Risk Assessment
- **Breaking Changes**: [List any]
- **Performance Impact**: [Expected effect]
- **Data Migration**: [Required/Not required]

### Rollback Plan
1. [Step 1]
2. [Step 2]
3. [Verification]

### Recommendation
[Go/No-Go with reasoning]
```

## Integration with Extended Thinking

When using these frameworks with extended thinking:

```python
# Enable extended thinking for complex reasoning
response = client.messages.create(
    model="claude-opus-4-5-20250514",
    max_tokens=16000,
    thinking={
        "type": "enabled",
        "budget_tokens": 15000  # Higher budget for complex reasoning
    },
    system="""You are a systematic problem solver. Use structured
    reasoning frameworks like Chain-of-Thought, Tree-of-Thought,
    or MECE analysis as appropriate for the problem.""",
    messages=[{
        "role": "user",
        "content": "Analyze this architecture decision using ToT..."
    }]
)
```

## Best Practices

1. **Choose the right framework**: CoT for linear problems, ToT for branching decisions
2. **Document your reasoning**: Makes it reviewable and repeatable
3. **Validate assumptions**: Each step should build on verified facts
4. **Consider alternatives**: Always explore at least 2-3 approaches
5. **Quantify when possible**: Use metrics to compare options
6. **Time-box exploration**: Set limits on analysis depth

## See Also

- [[extended-thinking]] - Enable deep reasoning capabilities
- [[deep-analysis]] - Analytical templates
- [[debugging]] - General debugging patterns
- [[testing]] - Validation strategies