
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 a polynomial $p(x)$ such that $p(2) = 6$ and $p(4) = 14$, express $p(x)$ in terms of another polynomial $q(x)$ such that $p(x) = q(x)(x-2)(x-4) + r(x)$, determine the polynomial $r(x)$, where $r(x)$ is a polynomial of degree less than 2.

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