
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 a graph of \( y = c \sec dx \) for some positive constants \( c \) and \( d \). Find \( c \).

[asy]
import TrigMacros;

size(500);

real h(real x)
{
    return 3*sec(x/4);
}

draw(graph(h, -2*pi + 0.01, -pi - 0.01), red);
draw(graph(h, -pi + 0.01, pi - 0.01), red);
draw(graph(h, pi + 0.01, 2*pi - 0.01), red);
limits((-2*pi, -5), (2*pi, 5), Crop);
draw((-pi, -5)--(-pi, 5), dashed);
draw((pi, -5)--(pi, 5), dashed);
trig_axes(-2*pi, 2*pi, -5, 5, pi/2, 1);
layer();
rm_trig_labels(-11, 11, 2);

label("$1$", (0,1), E);
label("$2$", (0,2), E);
label("$3$", (0,3), E);
label("$4$", (0,4), E);
label("$-1$", (0,-1), E);
label("$-2$", (0,-2), E);
label("$-3$", (0,-3), E);
label("$-4$", (0,-4), E);
[/asy]

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