
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 \( f: \mathbb{Z}_{>0} \rightarrow \mathbb{Z} \) be a function with the following properties:

(i) \( f(1)=0 \),

(ii) \( f(p)=1 \) for all prime numbers \( p \),

(iii) \( f(x y)=y f(x)+x f(y) \) for all \( x, y \) in \( \mathbb{Z}_{>0} \).

Determine the smallest whole number \( n \geq 2015 \) such that \( f(n)=n \).

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