
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 $A M C$ be an isosceles triangle with $M$ as the vertex and $\widehat{A M C}$ being an acute angle. Let $B$ be the point symmetric to $A$ with respect to $M$, and let $H$ be the foot of the altitude from vertex $C$ in triangle $A B C$. Suppose $A H = H M$. Calculate the values of the three angles in triangle $A B C$.

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