Let $f: \mathbb{N} \to \mathbb{N}$ be a function satisfying the following conditions:

- $f(ab) = f(a)f(b)$ whenever the greatest common divisor (GCD) of $a$ and $b$ is $1$.
- $f(p + q) = f(p) + f(q)$ whenever $p$ and $q$ are prime numbers.

Determine all possible values of $f(2002)$. Justify your answers.

Let's think step by step and output the final answer within \boxed{}.
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