
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
Paul and Sara are walking in the same direction, Sara at 4 feet per second and Paul at 2 feet per second, on parallel paths that are 250 feet apart. A large circular pond 150 feet in diameter is centered midway between their paths. At the instant when the pond first blocks their line of sight, they are 250 feet apart. Let $T$ be the time, in seconds, until Paul and Sara can see each other again. Provide $T$ expressed as a fraction in its lowest terms, and find the sum of the numerator and denominator.

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