
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 side \(AB\) of an equilateral triangle \(ABC\), a point \(K\) is chosen, and on side \(BC\), points \(L\) and \(M\) are chosen such that \(KL = KM\) and point \(L\) is closer to \(B\) than \(M\).

a) Find the angle \(MKA\) if it is known that \(\angle BKL = 10^\circ\).

b) Find \(MC\) if \(BL = 2\) and \(KA = 3\).

Provide justification for each part of the answers.

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