
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 \( M \) is the midpoint of edge \( AD \) of tetrahedron \( ABCD \). Point \( N \) lies on the extension of edge \( AB \) beyond point \( B \), and point \( K \) lies on the extension of edge \( AC \) beyond point \( C \), such that \( BN = AB \) and \( CK = 2AC \). Construct the cross-section of the tetrahedron with the plane \( MNK \). In what ratio does this plane divide the edges \( DB \) and \( DC \)?

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