
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 base of the pyramid \( DABC \) is an equilateral triangle \( ABC \) with a side length of \( 4\sqrt{2} \). A lateral edge \( DC \) is perpendicular to the base plane and has a length of 2. Find the angle and the distance between the skew lines, one of which passes through the point \( D \) and the midpoint \( M \) of the edge \( BC \), and the other passes through the point \( C \) and the midpoint \( K \) of the edge \( AB \).

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