
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
Consider the polynomial  $P(n) = n^3 -n^2 -5n+ 2$ . Determine all integers  $n$  for which  $P(n)^2$  is a square of a prime.

<details><summary>Remark.</summary>I'm not sure if the statement of this problem is correct, because if  $P(n)^2$  be a square of a prime, then  $P(n)$  should be that prime, and I don't think the problem means that.</details>

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