
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
The polynomial  $1976(x+x^2+ \cdots +x^n)$  is decomposed into a sum of polynomials of the form  $a_1x + a_2x^2 + \cdots + a_nx^n$ , where  $a_1, a_2, \ldots , a_n$  are distinct positive integers not greater than  $n$ . Find all values of  $n$  for which such a decomposition is possible.

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