
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 graph of the rational function \(\frac{p(x)}{q(x)}\) has a horizontal asymptote at \(y=0\) and a vertical asymptote at \(x=-2\). Given that \(p(3)=1\) and \(q(3)=4\), and knowing \(q(x)\) is quadratic, find the expression for \(p(x) + q(x)\).

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