
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 \( y = a \sin(bx + c) \) for some constants \( a < 0 \), \( b > 0 \), and \( c \). Find \( a \) and \( b \).

[asy]
import TrigMacros;
size(400);
real h(real x) { return (-3*sin(0.5*x + pi/4)); }
draw(graph(h,-12*pi,12*pi,n=700,join=operator ..),red);
trig_axes(-12*pi,12*pi,-4,4,pi,1);
layer();
rm_trig_labels(-5, 5, 3);
label("$3$", (0,3), E);
label("$-3$", (0,-3), E);
[/asy]

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