
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 the partial fraction decomposition of
\[
\frac{x^2 - 13}{x^3 - 3x^2 - 4x + 12}
\]
is expressed as
\[
\frac{A}{x-2} + \frac{B}{x+2} + \frac{C}{x-3}.
\]
Find the product $ABC$.

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