
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. They share a common vertex. Given that $XYZ$ is an isosceles triangle formed by connecting the vertices of the pentagon and triangle, find the measure of the angle indicated by the question mark. Assume the vertex with the question mark is shared by the triangle and pentagon, and it is opposite to the base of the isosceles triangle.

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