
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 $f(z) = c_3z^3 + c_2z^2 + c_1z + c_0$ and $g(z) = d_2z^2 + d_1z + d_0$ be two polynomials where $c_3 \neq 0$ and $d_2 \neq 0$. What is the degree of $f(z) + g(z)$ if $c_3 + d_2 \neq 0$?

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