
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
In the triangle \(ABC\), points \(K\), \(L\), and \(M\) are taken on sides \(AB\), \(BC\), and \(AD\) respectively. It is known that \(AK = 5\), \(KB = 3\), \(BL = 2\), \(LC = 7\), \(CM = 1\), and \(MA = 6\). Find the distance from point \(M\) to the midpoint of \(KL\).

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