
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 $y = a \cos (bx + c) + d$ for some positive constants $a,$ $b,$ $c,$ and $d.$  Find $b.$

[asy]import TrigMacros;

size(400);

real f(real x)
{
	return 3*cos(2*x + pi/2) + 4;
}

draw(graph(f,-2*pi,2*pi,n=700,join=operator ..),blue);
trig_axes(-2*pi,2*pi,-2,10,pi/2,1);
layer();
rm_trig_labels(-5,5, 2);

label("$5$", (0,5), E);
label("$6$", (0,6), E);
label("$7$", (0,7), E);
label("$8$", (0,8), E);
label("$9$", (0,9), E);
label("$10$", (0,10), E);
[/asy]

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