
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}
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