
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{R} $  be a function such that for all  $n > 1$  there is a prime divisor  $p$  of  $n$  such that \[ f(n)=f\left(\frac{n}{p}\right)-f(p). \] 
Furthermore, it is given that  $ f(2^{2014})+f(3^{2015})+f(5^{2016})=2013 $ . Determine  $ f(2014^2)+f(2015^3)+f(2016^5) $ .

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