
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
When the product
$$
\left(2021 x^{2021}+2020 x^{2020}+\cdots+3 x^{3}+2 x^{2}+x\right)\left(x^{2021}-x^{2020}+\cdots+x^{3}-x^{2}+x-1\right)
$$
is expanded and simplified, what is the coefficient of \(x^{2021}\)?

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