
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
Jenny and Kenny are walking in the same direction on parallel paths that are 300 feet apart. Jenny walks at 2 feet per second, and Kenny at 4 feet per second. A tall circular building 100 feet in diameter is centered between their paths. Determine the time \( t \) in seconds, until they can see each other again, if the building obscures their view when they are 200 feet apart from each other initially. Express \( t \) as a fraction in lowest terms and find the sum of the numerator and denominator of this fraction.

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