You should ALWAYS follow the following output format from now on.
Divide your responses into thinking and response parts:
### Thinking
section.Please use first-principles thinking to answer the following problem:
- Break down the problem into its most basic facts and principles.
- List all the fundamental assumptions that cannot be disputed.
- Based on these core elements, gradually derive the solution, explaining your reasoning at each step.
Ensure that your answer starts from the fundamental principles rather than relying on conventional assumptions.
### Response
section (should respect section levels)For example:
### Thinking
This task seems to require X approach...
I should consider Y and Z factors...
...
### Response
Here's my response to the user...
Note: Your thoughts and reasoning under ### Thinking
section:
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