
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
Below is the graph of $y = a \tan bx$, where $a$ and $b$ are positive constants. Determine $ab$.

[asy]import TrigMacros;
size(250);
real g(real x)
{
    return 3*tan(2*x);
}
draw(graph(g, -pi/4 + 0.01, pi/4 - 0.01),blue);
draw(graph(g, 3*pi/4 + 0.01, 5*pi/4 - 0.01),blue);
limits((-pi,-6),(pi,6),Crop);
draw((-pi/4,-6)--(-pi/4,6),dashed);
draw((pi/4,-6)--(pi/4,6),dashed);
trig_axes(-pi,pi,-6,6,pi/6,1);
layer();
rm_trig_labels(-7, 7, 6);

label("$3$", (0,3), E);
label("$6$", (0,6), E);
label("$-3$", (0,-3), E);
label("$-6$", (0,-6), E);
[/asy]

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