
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 $5 \cdot f(x) + 6 \cdot g(x) = k(x)$ where $f(x),$ $g(x),$ and $k(x)$ are all polynomials in $x$. If the degree of $f(x)$ is $10$ and the degree of $k(x)$ is $12$, what is the minimum possible degree of $g(x)$?

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