
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. Kenny's speed is 4 feet per second, while Jenny's speed is 2 feet per second. A circular building, 150 feet in diameter, is centered midway between their paths. At the moment when the building first obstructs their line of sight, the distance between Jenny and Kenny is 300 feet. Determine the time, $t$ in seconds, until they can see each other again, and find the sum of the numerator and denominator of $t$ when expressed in its lowest terms.

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