
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

Point \( K \) is located on edge \( AD \) of tetrahedron \( ABCD \), point \( N \) is on the extension of edge \( AB \) beyond point \( B \), and point \( M \) is on the extension of edge \( AC \) beyond point \( C \), with \( AK:KD = 3:1, BN = AB \), and \( CM:AC = 1:3 \). Construct the section of the tetrahedron with a plane passing through points \( K, M, N \). In what ratio does this plane divide the volume of the tetrahedron?

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