
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
How many polynomials of the form \( x^6 + ax^5 + bx^4 + cx^3 + dx^2 + ex + 2024 \), where \( a, b, c, d, e \) are real numbers, 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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