
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 $p(x)$ is linear and $q(x)$ is quadratic, is shown in the plot. Assume that the grid lines are at integers for a different range.

[asy]
unitsize(0.6 cm);

real func (real x) {
  return (3*x/((x - 1)*(x + 4)));
}

int i;

for (i = -6; i <= 6; ++i) {
  draw((i,-6)--(i,6),gray(0.7));
  draw((-6,i)--(6,i),gray(0.7));
}

draw((-6,0)--(6,0));
draw((0,-6)--(0,6));
draw((-4,-6)--(-4,6),dashed);
draw((1,-6)--(1,6),dashed);
draw(graph(func,-6,-4.1),red);
draw(graph(func,-3.9,0.9),red);
draw(graph(func,1.1,6),red);

limits((-6,-6),(6,6),Crop);
[/asy]

Given these modifications, find the value of $\frac{p(-2)}{q(-2)}.$

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