
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 that \( O \) is the circumcenter of \( \triangle ABC \), and \( X \) and \( Y \) are points on \( AC \) and \( AB \) respectively, such that \( BX \) and \( CY \) intersect at \( O \). Also, \(\angle BAC = \angle AYX = \angle XYC\). Find the measure of \(\angle BAC\).

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