
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
Two boys start at the same point A on an elliptical track and move in opposite directions. The speeds of the boys are 7 ft. per second and 11 ft. per second, respectively. The elliptical track has a major axis of 100 ft and a minor axis of 60 ft. Calculate the number of times they meet, excluding the start and finish, assuming they start at the same time and finish when they first meet at point A again.

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