
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 graph of the rational function $\frac{1}{p(x)}$ has vertical asymptotes at $x = -2$ and $x = 3$, and $p(x)$ is a quadratic polynomial. If it is known that $p(1) = -10$, find the polynomial $p(x)$.

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