
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
Let  $P(x)$  be a polynomial whose coefficients are all either  $0$  or  $1$ . Suppose that  $P(x)$  can be written as the product of two nonconstant polynomials with integer coefficients. Does it follow that  $P(2)$  is a composite integer?

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