
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 \(P A B C D\) is the parallelogram \(A B C D\). Point \(K\) is the midpoint of edge \(A P\), point \(N\) is located on edge \(C P\) such that \(C N : N P = 1 : 3\), and point \(M\) is located on the extension of edge \(B C\) beyond point \(B\) such that \(B M = 2 B C\). Construct the cross-section of the pyramid formed by the plane passing through points \(K\), \(M\), and \(N\). In what ratio does this plane divide the volume of the pyramid?

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