
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
The rectangle \(ABCD\) is such that \(AD = 2AB\). Point \(M\) is the midpoint of side \(AD\). Inside the rectangle, there is a point \(K\) such that \(\angle AMK = 80^\circ\) and the ray \(KD\) is the angle bisector of \(\angle MKC\). How many degrees is the angle \(KDA\)?

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