
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
The function \( f(x) \) is such that for every natural number \( n > 1 \), there exists a prime divisor \( p \) of the number \( n \) such that

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

It is known that \( f(1001) = 1 \). What is \( f(1002) \)?

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