
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 any positive integer  $x$ , let  $f(x)=x^x$ . Suppose that  $n$  is a positive integer such that there exists a positive integer  $m$  with  $m  \neq 1$  such that  $f(f(f(m)))=m^{m^{n+2020}}$ . Compute the smallest possible value of  $n$ .

*Proposed by Luke Robitaille*

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