
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 children stood equally spaced on a circle of radius 50 feet. Each child walked to all of the other non-adjacent children on the circle, shook hands, and then returned to their original spot on the circle before the next child started their trip. After all eight children completed this, what is the least distance in feet that could have been traveled by all children combined? Express your answer in terms of π and simplest radical form.

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