
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
Determine those polynomials $f(x)$ for which there exists a polynomial $p(t)$ that satisfies the identity

$$
f\left(x^{2}\right) = p(f(x)).
$$

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