
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
Let  $r_1, r_2, ..., r_{2021}$  be the not necessarily real and not necessarily distinct roots of  $x^{2022} + 2021x = 2022$ . Let  $S_i = r_i^{2021}+2022r_i$  for all  $1 \le i \le 2021$ . Find  $\left|\sum^{2021}_{i=1} S_i \right| = |S_1 +S_2 +...+S_{2021}|$ .

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