
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
There is a hypothesis that the expression

$$
(x+a)(x+2a)(x+3a)(x+4a) + a^4
$$

is the square of a polynomial of the form \( x^2 + px + q a^2 \). How can this claim be verified and how can the coefficients \( p \) and \( q \) be found?

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