
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
Points \( K, M, \) and \( N \) are located on the edges \( BC, AD, \) and \( CD \) of tetrahedron \( ABCD \), respectively, such that \( BK: KC = 1:3 \), \( AM: MD = 3:1 \), and \( CN: ND = 1:2 \). Construct the cross-section of the tetrahedron with the plane passing through points \( K, M, \) and \( N \). 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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