
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 along distinct paths that are 210 feet apart towards the same direction in parallel manner. Jenny walks at a speed of 2 feet per second, and Kenny at a speed of 3.5 feet per second. A circular building with a diameter of 100 feet is centered precisely midway between their paths. At a certain instant when the building just obstructs the view between Jenny and Kenny, they are separated by 210 feet. Calculate the time $t$ in seconds before they can see each other again without obstruction, where $t$ should be expressed as a fraction reduced to its lowest terms. What is the sum of the numerator and denominator of $t$?

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