
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
For the polynomial
\[ p(x) = 985 x^{2021} + 211 x^{2020} - 211, \]

let its 2021 complex roots be \( x_1, x_2, \cdots, x_{2021} \). Calculate
\[ \sum_{k=1}^{2021} \frac{1}{x_{k}^{2} + 1} = \]


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