
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

Given a parallelogram \(ABCD\), and point \(M\) is the midpoint of side \(BC\). On side \(AD\), there is a point \(K\) such that \(BK = BM\) and quadrilateral \(KBMD\) is cyclic.

(a) Find the length of segment \(MD\) if \(AD = 15\).

(b) What is the measure of angle \(KMD\) if \(\angle BAD = 43^\circ\)?

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