
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 $\frac{1}{q(x)}$, where $q(x)$ is a quadratic polynomial, and it's known that $q(2) = 2$. Further, there are vertical asymptotes at $x = -1$ and $x = 1$. Additionally, $q(1) = 0$. Determine the quadratic polynomial $q(x)$.

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