
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's say that James and Sara each think of a polynomial. Each of their polynomials is monic, has degree 4, and has the same positive coefficient for the term $z^3$ and the same positive constant term. The product of their polynomials results in \[z^8 + 4z^7 + 5z^6 + 7z^5 + 9z^4 + 8z^3 + 6z^2 + 8z + 9.\] Determine the constant term of Sara's polynomial.

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