
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
In a tetrahedron \(A B C D\), a plane is drawn through the midpoint \(M\) of edge \(A D\), vertex \(C\), and point \(N\) on edge \(B D\) such that \(B N: N D = 2: 1\). In what ratio does this plane divide the segment \(K P\), where \(K\) and \(P\) are the midpoints of edges \(A B\) and \(C D\) respectively?

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