
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
Given that $5 \cdot p(x) + 6 \cdot q(x) = r(x)$ where $p(x),$ $q(x),$ and $r(x)$ are polynomials in $x.$ If the degree of $p(x)$ is $10$ and the degree of $r(x)$ is $12$, determine the minimum possible degree of $q(x)$.

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