
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 \( M, N \), and \( K \) belong respectively to the edges \( AD \), \( AB \), and \( BC \) of tetrahedron \( ABCD \), where \( AM: MD = 2:3 \), \( BN: AN = 1:2 \), and \( BK = KC \). Construct the cross section of the tetrahedron by a plane passing through points \( M, N, K \). In what ratio does this plane divide edge \( CD \)?

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