
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 a right-angled triangle \(ABC\), the altitude \(CH\) is drawn from the vertex of the right angle. From point \(N\) on leg \(BC\), a perpendicular \(NM\) is dropped to the hypotenuse. The line \(NA\) is perpendicular to \(CM\) and \(MH:CH = 1:\sqrt{3}\). Find the acute angles of triangle \(ABC\).

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