
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
Two circles with radii 1 and 2 have a common center at point \( O \). Vertex \( A \) of the equilateral triangle \( ABC \) is on the larger circle, and the midpoint of side \( BC \) is on the smaller circle. What can be the measure of angle \( BOC \)?

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