
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 rectangular prism $A B C D-A_{1} B_{1} C_{1} D_{1}$ with $A A_{1}=2$, $A D=3$, and $A B= 251$, the plane $A_{1} B D$ intersects $C C_{1}$, $C_{1} B_{1}$, and $C_{1} D_{1}$ at points $L$, $M$, and $N$ respectively. Find the volume of the tetrahedron $C_{1} L M N$.

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