
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
An equilateral triangle and a regular pentagon are inscribed in a circle as shown. $ABC$ is isosceles. The triangle and pentagon share a common vertex. Calculate the measure of the angle indicated by the question mark.

[asy]
import markers; defaultpen(linewidth(0.8));
pair A,B,C,D,E,F,G,H,I;

draw(unitcircle);

A=(-1,0);
B=dir(162);
C=dir(234);
D=dir(306);
E=(1,0);
F=dir(90);

draw(A--B--C--D--E--A);

G=dir(18);
H=dir(90);
I=dir(162);

draw(H--G--I--H);

G=dir(54);

markangle(Label("?"),n=1,radius=10,H,G,A,marker(stickframe(n=0),true));

label("$A$",A,W);
label("$B$",B,NW);
label("$C$",C,SW);
label("$D$",D,SE);
label("$E$",E,E);
label("$G$",G,E);
label("$H$",H,N);
label("$I$",I,NW);
[/asy]

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