
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 the necessary and sufficient condition for the fourth-degree polynomial

$$
f(x)=A x^{4}+B x^{3}+C x^{2}+D x+E \quad(A \neq 0)
$$

to be expressible in the form

$$
f(x)=p(q(x))
$$

where $p(x)$ and $q(x)$ are quadratic polynomials.

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