
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) Find all positive integers  $n$  for which the equation  $(a^a)^n = b^b$  has a solution
in positive integers  $a,b$  greater than  $1$ .
(b) Find all positive integers  $a, b$  satisfying  $(a^a)^5=b^b$ 

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