
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 \( K \) is the midpoint of edge \( A A_{1} \) of cube \( A B C D A_{1} B_{1} C_{1} D_{1} \), and point \( L \) lies on edge \( B C \). Segment \( K L \) touches the sphere inscribed in the cube. In what ratio does the point of tangency divide segment \( K L \)?

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