
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
$ABCDEFGHIJ$ is a rectangular prism with $AB = 2$, $BC = 3$, $AE = 4$. Find $\sin \angle GAC$.

[asy]
import three;
triple A, B, C, D, EE, F, G, H;
A = (0, 0, 0);
B = (2, 0, 0);
C = (2, 3, 0);
D = (0, 3, 0);
EE = (0, 0, 4);
F = B + EE;
G = C + EE;
H = D + EE;
draw(B--C--D--A--cycle);
draw(EE--F--G--H--EE);
draw(A--EE,dashed);
draw(B--F);
draw(C--G);
draw(D--H);
draw(dashed, G--A--C);
label("$A$", A, SW);
label("$B$", B, SE);
label("$C$", C, NE);
label("$D$", D, NW);
label("$E$", EE, S);
label("$F$", F, E);
label("$G$", G, N);
label("$H$", H, W);
[/asy]

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