
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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