
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
A parallelepiped $A B C D A_1 B_1 C_1 D_1$ is given. Points $M, L$, and $K$ are taken on the edges $A D, A_1 D_1$, and $B_1 C_1$ respectively, such that $B_1 K = \frac{1}{3} A_1 L$ and $A M = \frac{1}{2} A_1 L$. It is known that $K L = 2$. Find the length of the segment by which the plane $K L M$ intersects the parallelogram $A B C D$.

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