
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 the give functions in  $\mathbb{N}$ :**(a)** Euler's  $\phi$  function ( $\phi(n)$ - the number of natural numbers smaller than  $n$  and coprime with  $n$ );**(b)** the  $\sigma$  function such that the  $\sigma(n)$  is the sum of natural divisors of  $n$ .
solve the equation  $\phi(\sigma(2^x))=2^x$ .

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