
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 parallelepiped $A B C D A_{1} B_{1} C_{1} D_{1}$. On the rays $C_{1}C$, $C_{1}B_{1}$, and $C_{1}D_{1}$, segments $C_{1}M$, $C_{1}N$, and $C_{1}K$ are laid out, respectively equal to $\frac{5}{2}C C_{1}$, $\frac{5}{2}C_{1} B_{1}$, and $\frac{5}{2}C_{1} D_{1}$. In what ratio does the plane passing through points $M$, $N$, $K$ divide the volume of the parallelepiped $A B C D A_{1} B_{1} C_{1} D_{1}$?

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