
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
Consider a scenario where Jenny and Kenny are walking in the same direction, with Kenny walking at 4 feet per second and Jenny at 1 foot per second, on parallel paths that are 300 feet apart. At the center between their paths is a circular building with a diameter of 150 feet. When the building first blocks their line of sight, they are 300 feet apart. Determine the time \( t \) in seconds before they can see each other again, and find 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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