
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, with Kenny moving at 4 feet per second and Jenny at 2 feet per second. A circular building with a diameter of 200 feet is centered between their paths. At a particular moment, the building blocks their line of sight when they are 300 feet apart. Determine the time, $t$, in seconds, before they can see each other again. What is the sum of the numerator and denominator if $t$ is expressed in lowest terms?

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