
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
For any positive integer \( k \), denote the sum of digits of \( k \) in its decimal representation by \( S(k) \). Find all polynomials \( P(x) \) with integer coefficients such that for any positive integer \( n \geq 2016 \), the integer \( P(n) \) is positive and 
\[ S(P(n)) = P(S(n)). \]

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