
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
Consider a circle with an equilateral triangle and a regular pentagon inscribed in it. The triangle and pentagon share a common vertex. Label the vertices of the triangle as $A$, $B$, and $C$ where $A$ is the shared vertex, and the vertices of the pentagon as $A$, $P_1$, $P_2$, $P_3$, $P_4$ in clockwise order. Calculate the measure of $\angle BAC$ within the triangle.

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