
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
A positive integer  $m$  is perfect if the sum of all its positive divisors,  $1$  and  $m$  inclusive, is equal to  $2m$ . Determine the positive integers  $n$  such that  $n^n + 1$  is a perfect number.

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