
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
On the edges \(AB\), \(BC\), and \(AD\) of the tetrahedron \(ABCD\), points \(K\), \(N\), and \(M\) are chosen, respectively, such that \(AK:KB = BN:NC = 2:1\) and \(AM:MD = 3:1\). Construct the section of the tetrahedron by the plane passing through points \(K\), \(M\), and \(N\). In what ratio does this plane divide edge \(CD\)?

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