
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
The altitudes of a scalene acute triangle \(ABC\) intersect at point \(H\). \(O\) is the circumcenter of triangle \(BHC\). The incenter \(I\) of triangle \(ABC\) lies on the segment \(OA\). Find the angle \(BAC\).

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