
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
Find the remainder when a polynomial $p(x)$ is divided by $(x-1)(x-3)(x-5)$. We are given that $p(1) = 4$, and $p(3) = 6$, and $p(5) = 8$.
A) $x + 2$
B) $x + 3$
C) $x^2 + x + 1$
D) $2x + 3$

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