Think

Activate deep analysis mode to reason through complex problems with extended multi-step thinking.

## Steps


1. Read the user's problem statement carefully. Identify the core question and any constraints.
2. Break the problem into sub-problems:
3. For each sub-problem, reason through possible approaches:
4. Evaluate trade-offs between approaches using criteria:
5. Synthesize findings into a coherent solution with clear reasoning chain.
6. Validate the solution by checking it against the original constraints.
7. Present the analysis with confidence level (high/medium/low).

## Format


```
Problem: <restated problem>
Sub-problems: <numbered list>
Analysis: <reasoning for each sub-problem>
Solution: <recommended approach>
```


## Rules

- Spend at least 60% of effort on understanding the problem before solving it.
- Never jump to the first solution that comes to mind.
- Always consider what could go wrong with the chosen approach.