
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 fly starts on the edge of a circular room with a radius of 100 feet. It first walks along the ceiling, passing through the center, to the opposite edge of the circle. It then progresses to a third point on the circle's edge making a straight line but not passing through the center again. The path from this third point back to the starting point is 120 feet. Determine the total feet the fly traveled.

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