
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]


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Let  $P(x)$  be a polynomial with integer coefficients, leading coefficient 1, and  $P(0) = 3$ . If the polynomial  $P(x)^2 + 1$  can be factored as a product of two non-constant polynomials with integer coefficients, and the degree of  $P$  is as small as possible, compute the largest possible value of  $P(10)$ .

*2016 CCA Math Bonanza Individual #13*

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