
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
Two right triangles ABT and ACK are constructed externally with respect to the sides \( AB \) and \( AC \) of triangle \( \mathrm{ABC} \) such that \( \angle ATB = \angle AKC = 90^{\circ} \) and \( \angle ABT = \angle ACK = 30^{\circ} \). A point \( M \) is chosen on the side \( \mathrm{BC} \) such that \( \mathrm{BM} = \mathrm{MC} \). Determine the measure of the angle \( \angle KMT \).

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