
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
Rectangle \(A B C D\) has the property that \(A D = 2 A B\). Point \(M\) is the midpoint of side \(A D\). Inside the rectangle, there is a point \(K\) such that \(\angle A M K = 80^\circ\) and ray \(K D\) is the angle bisector of \(\angle M K C\). How many degrees is the angle \(K D A\)?

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