
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
Determine all polynomials \( P(x) \) with real coefficients that satisfy the following two conditions:

(a) \( P(2017)=2016 \) and

(b) \( (P(x)+1)^{2}=P\left(x^{2}+1\right) \) for all real numbers \( x \).

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