
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
Eight boys stood equally spaced on a circle of radius 50 feet. Each boy walked to the boy exactly opposite to him on the circle (creating a diameter), shook hands, and then returned to his original spot. What is the least distance in feet that could have been traveled collectively by all boys? Express your answer in simplest form.

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