
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 \( AMC \) be an isosceles triangle with \( M \) as the vertex of the equal sides and \( \angle AMC \) as an acute angle. Let \( B \) be the symmetric point of \( A \) with respect to \( M \), and let \( H \) be the foot of the altitude from \( C \) in triangle \( ABC \). It is given that \( AH = HM \). Calculate the values of the three angles of triangle \( ABC \).

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