
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 and share a common vertex. $ABC$ is isosceles with $AB = BC$. The triangle and pentagon share vertex $A$. Determine the measure of the angle indicated by the question mark at vertex $A$.

[asy]
import markers; defaultpen(linewidth(0.8));
pair A,B,C,D,E,F,G;
draw(unitcircle);
A=dir(150);
B=dir(210);
C=dir(270);
D=dir(330);
E=dir(30);
draw(A--B--C--D--E--A);
F=dir(110);
G=dir(190);
draw(A--F--G--A);
markangle(Label("?"),n=1,radius=10,A,G,F,marker(stickframe(n=0),true));
label("$A$",A,NW);
label("$B$",G,SW);
label("$C$",F,NE);
[/asy]

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