
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
Consider two friends, Anna and Bella, each thinking of a monic polynomial of degree 3. Both polynomials have the same positive constant term and the same coefficient for $z^2$. The product of their polynomials is \[z^6 + 2z^5 + 5z^4 + 10z^3 + 10z^2 + 8z + 9.\] What is the constant term of Bella's polynomial?

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