
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
Construct the cross-section of a triangular pyramid \( A B C D \) with a plane passing through the midpoints \( M \) and \( N \) of edges \( A C \) and \( B D \) and the point \( K \) on edge \( C D \), for which \( C K: K D = 1: 2 \). In what ratio does this plane divide edge \( A B \)?

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