
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
Given a polynomial of the form $x^6 + ax^5 + bx^4 + cx^3 + dx^2 + ex + 2021$, where $a$, $b$, $c$, $d$, and $e$ are real numbers, determine the number of such polynomials that have the property that whenever $r$ is a root, so is $i \cdot r$.

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