
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 angle bisectors $A M$ and $B H$ of a triangle $A B C$ intersect at point $O$. It is known that $A O : M O = \sqrt{3}$ and $H O : B O = \sqrt{3} - 1$. Find the angles of triangle $A B C$.

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