
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 $f(x) = -3x^5 + 2x^4 - 7x^3 + x^2 + 5$, and $g(x)$ is another polynomial. If the highest degree of the polynomial $f(x) + g(x)$ is 2, what is the degree of $g(x)$ assuming $g(x)$ must cancel out certain terms in $f(x)$?

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