
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
A parabola with the equation $y=ax^2+bx+c$ is graphed below:

[asy]
xaxis(-3,7);
yaxis(-5,32);
real g(real x)
{
return 3(x-3)^2-9;
}
draw(graph(g,-1,5));
dot((3,-9));
label("Vertex: $(3,-9)$", (3,-9), SE);
dot((5,6));
label("$(5,6)$", (5,6), E);
[/asy]

The zeros of the quadratic $ax^2 + bx + c$ are at $x=p$ and $x=q$, where $p>q$. What is $p-q$?

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