
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
A regular pentagon and an equilateral triangle are inscribed in a circle. They share a common vertex. Label the vertices of the triangle as $X, Y, Z$ and consider the pentagon vertices as $A, B, C, D, E$ such that $A$ is the common vertex. If $\angle ZAX$ is the angle at the shared vertex within the triangle, find the measure of this angle.

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