
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
In the expansion of
\[
\left(1 + x + x^2 + \cdots + x^{20}\right)\left(1 + x + x^2 + \cdots + x^{10}\right)^2,
\]
what is the coefficient of \(x^{21}\)?
A) 156
B) 78
C) 253
D) 97
E) 435

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