
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
On the sides $\mathrm{AB}$ and $\mathrm{AC}$ of the right triangle $\mathrm{ABC}\left(\angle B C A=90^{\circ}\right)$, right triangles $\mathrm{ABT}$ and $\mathrm{ACK}$ are constructed externally so that $\angle A T B=\angle A K C=90^{\circ}$ and $\angle A B T=\angle A C K=60^{\circ}$. A point $\mathrm{M}$ is chosen on the side $\mathrm{BC}$ such that $\mathrm{BM}=\mathrm{MC}$. Determine the degree measure of the angle $\mathrm{KMT}$.

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