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

[asy]
import TrigMacros;

size(400);

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

draw(graph(f,-3*pi,3*pi,n=700,join=operator ..),red);
trig_axes(-3*pi,3*pi,-4,8,pi/2,1);
layer();
rm_trig_labels(-5,5, 2);

label("$3$", (0,3), E);
label("$5$", (0,5), E);
label("$7$", (0,7), E);
label("$1$", (0,1), E);
[/asy]

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