
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
Let \( ABC \) be a triangle in which \( \angle ABC = 60^\circ \). Let \( I \) and \( O \) be the incentre and circumcentre of \( ABC \), respectively. Let \( M \) be the midpoint of the arc \( BC \) of the circumcircle of \( ABC \), which does not contain the point \( A \). Determine \( \angle BAC \) given that \( MB = OI \).

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