
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 share a vertex and are inscribed in a circle. The triangle and pentagon share no other vertices. They intersect at another point creating an additional vertex of a new triangle inside the circle. If given the side of the pentagon touches the non-shared vertex of the equilateral triangle, find the angle at the vertex shared by the pentagon, triangle, and the intersection point inside.

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