
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  $P(x) \in \mathbb R[x]$  satisfying the following two conditions :
(a)  $P(2017) = 2016$  and
(b)  $(P(x) + 1)^2 = P(x^2 + 1)$  for all real numbers  $x$ .
 
*proposed by Walther Janous*

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