
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
For a natural number  $m>1$  we'll denote with  $f(m)$  the sum of all natural numbers less than  $m$ , which are also coprime to  $m$ . Find all natural numbers  $n$ , such that there exist natural numbers  $k$  and  $\ell$  which satisfy  $f(n^{k})=n^{\ell}$ .

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