
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 $y = a \sin bx$ for some constants $a < 0$ and $b > 0.$  Redraw the graph for $a = -3$ and $b = \frac{1}{2}$, and find $a.$

[asy]
import TrigMacros;

size(400);

real g(real x)
{
    return (-3*sin(0.5*x));
}

draw(graph(g,-12*pi,12*pi,n=700,join=operator ..),red);
trig_axes(-12*pi,12*pi,-4,4,3*pi,1);
layer();
rm_trig_labels(-5, 5, 2);

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

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