
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
Point $B$ lies between points $A$ and $C$. In the half-plane with boundary $(AC)$, points $K$ and $H$ are such that $A K = K B$, $B H = H C$, $\angle A K B = \alpha$, and $\angle B H C = \pi - \alpha$. Find the angles of triangle $K H M$, where $M$ is the midpoint of segment $A C$.

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