
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 integer $n \geq 2015$ such that $f(n)=n$.

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