
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 a polynomial $p(x)$ satisfy $p(2) = 6$ and $p(4) = 10$. Additionally, it is known that when $p(x)$ is divided by $(x-2)(x-4)$, the remainder is a linear polynomial $r(x)$. Find $r(x)$.
A) $x + 3$
B) $3x + 1$
C) $2x + 2$
D) $x + 2$

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