
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 polynomial $p(x)$ be divided by $x - 1$, resulting in a remainder of 4. When $p(x)$ is divided by $x - 2$, the remainder is -3. Additionally, when $p(x)$ is divided by $x + 3$, the remainder is 1. Find the remainder when $p(x)$ is divided by $(x - 1)(x - 2)(x + 3)$.

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