
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system

Let \( f \) be a real-valued function defined on the positive integers satisfying the following condition: For all \( n > 1 \) there exists a prime divisor \( p \) of \( n \) such that

\[ f(n) = f\left(\frac{n}{p}\right) - f(p) \]

Given that \( f(2001) = 1 \), what is the value of \( f(2002) \)?

Present the answer in LaTex format: \boxed{Your answer}
user