
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 polynomial  $P(x)\in \mathbb{R}[x]$  satisfying the following two conditions:
(a)  $P(2017)=2016$  and
(b)  $(P(x)+1)^2=P(x^2+1)$  for all real number  $x$ .

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