
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 pentagon and an equilateral triangle are both inscribed in a circle. They share one common vertex. Label this shared vertex as $X$, and the adjacent vertices in the pentagon from $X$ in the clockwise direction as $Y$ and $Z$. Label the vertices of the equilateral triangle such that $A$ is at $X$ and $B$ and $C$ on either side. If $\angle BXC$ is marked with a question mark, what is the number of degrees in the measure of $\angle BXC$?

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