
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 $y = a \cos bx$ for some constants $a > 0$ and $b > 0$. Find $a$.

[asy]
import TrigMacros;

size(400);

real g(real x) 
{
    return (3*cos(2*x));
}

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

label("$1$", (0,1), E);
label("$3$", (0,3), E);
label("$-1$", (0,-1), E);
label("$-3$", (0,-3), E);
[/asy]

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