
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
The integers $P$ and $Q$ are chosen such that
\[\frac{P}{x+6}+\frac{Q}{x^2-6x}=\frac{x^2-3x+12}{x^3+x^2-24x}\]
for all real values of $x$ except $-6$, $0$, and $6$. Find $Q/P$.

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