
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
A polynomial $p(x)$ of degree $17$ is divided by a polynomial $g(x)$, resulting in a quotient polynomial of degree $9$ and a remainder of $5x^5 + 2x^3 - 3x + 7$. What is $\deg g$?

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