
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
Find all functions  $f$  defined on the integers greater than or equal to  $1$  that satisfy:
(a) for all  $n,f(n)$  is a positive integer.
(b)  $f(n + m) =f(n)f(m)$  for all  $m$  and  $n$ .
(c) There exists  $n_0$  such that  $f(f(n_0)) = [f(n_0)]^2$  .

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