
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
A polynomial  $f(x)$  with real coefficients is called *generating*, if for each polynomial  $\varphi(x)$  with real coefficients there exists a positive integer  $k$  and polynomials  $g_1(x),\dotsc,g_k(x)$  with real coefficients such that
\[\varphi(x)=f(g_1(x))+\dotsc+f(g_k(x)).\]
Find all generating polynomials.

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