
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 \(y = \frac{p(x)}{q(x)}\) displays a horizontal asymptote at \(y = 3\) and a vertical asymptote at \(x = -3\). A hole is detected at \(x = 6\). This graph crosses the x-axis at \(x = 2\). Determine \(\frac{p(4)}{q(4)}\).

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