
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
Given a triangle \( ABC \) with an excircle centered at \( O \), which touches side \( BC \) and the extensions of sides \( AB \) and \( AC \). Point \( O_1 \) is the reflection of point \( O \) with respect to line \( BC \). Determine the measure of angle \( A \) if it is known that point \( O_1 \) lies on the circumcircle of triangle \( ABC \).

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