
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. Between their paths are two circular buildings, each 150 feet in diameter, positioned 200 feet apart from each other, measured from their centers, which are aligned with the midpoint of the paths. At the instant when the first building blocks the view between Jenny and Kenny, they are 250 feet apart. Let $t$ be the time, in seconds, before Jenny and Kenny can see each other once they are past the second building. If $t$ is written as a fraction in lowest terms, what is the sum of the numerator and denominator?

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