
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 altitude \(AH\) and the angle bisector \(CL\) of triangle \(ABC\) intersect at point \(O\). Find the angle \(BAC\) if it is known that the difference between the angle \(COH\) and half of the angle \(ABC\) is \(46^\circ\).

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