
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 start walking in the same direction with Kenny walking at 4 feet per second and Jenny at 2 feet per second along parallel paths that are 100 feet apart. A circular building with a diameter of 100 feet is centered between their paths. At the moment their views of each other are initially blocked by the building, they are 300 feet apart. Determine the time $t\,$ in seconds after which they can see each other again, and find the sum of the numerator and denominator of $t\,$ in its lowest terms.

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