
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 rectangular prism-shaped box has two end faces that are right-angled trapezoids, with the distance between the parallel sides being \( d \). The box is placed on a flat cart according to the diagram. The width \( k \) of the cart's surface is greater than \( d \). To prevent the box from sliding, it is tied with a stretched rope that passes over it; the three sections of the rope lie in a plane perpendicular to the side edges, and the ends of the rope are fixed to the longitudinal edges of the cart. What should be the distance of the supporting side edges of the box from the longitudinal edges of the cart's surface to ensure that the rope does not loosen due to lateral displacement of the box?

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