
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 \( \Delta ABC \) be a non-isosceles acute-angled triangle with circumcenter \( O \), orthocenter \( H \), and \( \angle C = 41^\circ \). Suppose the bisector of \( \angle A \) passes through the midpoint \( M \) of \( OH \). Find \( \angle HAO \) in degrees.

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