
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
In a rectangular prism, the three edges meeting at one vertex have different lengths. Select a pair of skew edges and then find, on each of the 12 edges of the prism, the point for which the sum of the distances from the selected edges is minimized. What is the volume of the convex body whose vertices are the points thus found?

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