
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 polynomials $f(z)$ and $g(z)$, where $f(z)$ has a degree of three and $g(z)$ has a degree of two. The coefficient of the highest degree term of $f(z)$ becomes zero if $z = 1$. What is the degree of $f(z) + g(z)$ when $z = 1$?

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