
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 $y = \frac{p(x)}{q(x)}$, where $p(x)$ and $q(x)$ are quadratic. Identify the value of $\frac{p(4)}{q(4)}$, given the following information:
- The rational function has a vertical asymptote at $x = -1$.
- The rational function has a horizontal asymptote, $y = -3$.
- There is a hole in the graph at $x = 6$.
- The graph intersects with the x-axis at $(2,0)$.

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