
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 right triangles \(MDC\) and \(ADK\) have a common right angle at \(D\). Point \(K\) lies on \(CD\) and divides it in the ratio \(2:3\) from point \(C\). Point \(M\) is the midpoint of side \(AD\). Find the sum of the degree measures of angles \(AKD\) and \(MCD\), given that \(AD : CD = 2:5\).

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