
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
Consider the series expansion of
\[\left(1 + x + x^2 + \cdots + x^{30}\right)\left(1 + x + x^2 + \cdots + x^{18}\right)^2.\]
Find the coefficient of \(x^{31}\).
A) 709
B) 644
C) 528
D) 182
E) 91

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