
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
Steven and Linda are jogging in the same direction on parallel paths, with Steven jogging at 4 feet per second and Linda at 2 feet per second. Parallel paths are 300 feet apart. A round stadium with a diameter of 200 feet is centered midway between their paths. The moment the stadium obscures their line of sight, they are 300 feet apart in terms of the direction of their motion. Let $t$ denote the time in seconds from when they lose sight of each other till the time they can see each other again. Write $t$ as a fraction in lowest terms and find the sum of its numerator and denominator.

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