
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 \( S \) be the function that associates to a natural number \( n \) the sum of its digits. Find all polynomials with integer coefficients \( P \) such that

$$
\forall n \geqslant 2016, P(n)>0 \text { and } S(P(n))=P(S(n))
$$

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