
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
Suppose $f(z)$ and $g(z)$ are polynomials in $z$, and the degree of $g(z)$ is two. If the degree of $f(z)$ is three, what is the degree of $f(z) + g(z)$? Assume the leading coefficient of $g(z)$ is such that when added to the leading coefficient of $f(z)$ for the highest degree term, it does not zero out.

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