
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
Aiden and Bella each think of a polynomial. Each of their polynomials is monic, one has a degree of 3 and another has a degree of 5, both have the same negative constant term, and the leading coefficient of $x$. The product of their polynomials is \[x^8 + 2x^7 + x^6 + 2x^5 + 3x^4 + 2x^3 + x^2 + 2x + 9.\] What is the absolute value of the constant term of Bella's polynomial?

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