
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
In an acute-angled triangle \( ABC \), the angle bisector \( AN \), the altitude \( BH \), and the line perpendicular to side \( AB \) passing through its midpoint intersect at a single point. Find angle \( BAC \).

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