
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 walks at 4 feet per second and Jenny at 2 feet per second. A circular building 150 feet in diameter is centered midway between their paths. At the initial moment when the building blocks their line of sight, they are 300 feet apart. Determine the time $t$, in seconds, before Jenny and Kenny can see each other again. If $t$ is expressed as a fraction in its simplest form, what is the sum of the numerator and denominator?

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