
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
Find all polynomials  $p(x)$  with real coefficients that have the following property: there exists a polynomial  $q(x)$  with real coefficients such that   $$ p(1) + p(2) + p(3) +\dots + p(n) = p(n)q(n) $$   for all positive integers  $n$ . 

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