
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
A polynomial $p(x)$ leaves a remainder of 2 when divided by $x - 3$, a remainder of -2 when divided by $x + 1$, and a remainder of 5 when divided by $x - 4$. Let $r(x)$ be the remainder when $p(x)$ is divided by $(x - 3)(x + 1)(x - 4)$. Find $r(5)$.

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