
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 which  $ p$  prime numbers, there is an integer root of the polynominal  $ 1 \plus{} p \plus{} Q(x^1)\cdot\ Q(x^2)\ldots\ Q(x^{2p \minus{} 2})$  such that  $ Q(x)$  is a polynominal with integer coefficients?

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