
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
$ABCDEFGH$ shown below is a cube where each edge has length $2$. Find $\sin \angle BAG$.

[asy]
import three;

triple A,B,C,D,E,F,G,H;

A = (0,0,0);
B = (2,0,0);
C = (2,2,0);
D= (0,2,0);
E = (0,0,2);
F = B+E;
G = C + E;
H = D + E;
draw(B--C--D);
draw(B--A--D,dashed);
draw(E--F--G--H--E);
draw(A--E,dashed);
draw(B--A--G,dashed);
draw(B--F);
draw(C--G);
draw(D--H);
label("$A$",A,S);
label("$B$",B,W);
label("$C$",C,S);
label("$D$",D,E);
label("$E$",E,N);
label("$F$",F,W);
label("$G$",G,SW);
label("$H$",H,E);
[/asy]

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