
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 \( ABCD \) with point \( M \) as the midpoint of side \( BC \). On side \( AD \), point \( K \) is chosen such that \( BK = BM \) and quadrilateral \( KBMD \) is inscribed in a circle.

(a) What is the length of segment \( MD \) if \( AD = 19 \)?

(b) What is the measure of angle \( KMD \) if \( \angle BAD = 44^\circ \)?

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