
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
Given a tetrahedron \(ABCD\). Points \(M\), \(N\), and \(K\) lie on edges \(AD\), \(BC\), and \(DC\) respectively, such that \(AM:MD = 1:3\), \(BN:NC = 1:1\), and \(CK:KD = 1:2\). Construct the section of the tetrahedron with the plane \(MNK\). In what ratio does this plane divide the edge \(AB\)?

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