
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
Kate and Lee are walking towards each other, Lee at 4 feet per second and Kate at 2 feet per second, along parallel paths that are 300 feet apart. A circular monument 150 feet in diameter is centered midway between their paths. When Kate and Lee first see each other past one edge of the monument, they are 500 feet apart along the parallel tracks. How long, in seconds, will it take till Kate and Lee can see each other clearly again, once blocked by the monument? Express your answer as a fraction in lowest terms and find the sum of the numerator and denominator.

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