
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, Kenny at 4 feet per second and Jenny at 2 feet per second, on parallel paths that are 300 feet apart. A tall circular building 150 feet in diameter is centered midway between their paths. At the instant when the building first blocks their line of sight, they are 300 feet apart. Let $t$ be the amount of time, in seconds, before Jenny and Kenny can see each other again. Calculate $t$ and find the sum of the numerator and denominator of $t$ when it is expressed as a fraction in lowest terms.

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