
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
Lucy and Tom are walking in the same direction on parallel paths that are 300 feet apart. Tom walks at 4 feet per second and Lucy at 2 feet per second. A circular building with a diameter of 150 feet is centered midway between the paths. At a certain instant, the building starts blocking the line of sight between Lucy and Tom. Determine the amount of time, in seconds, before Lucy and Tom can see each other again. Express this time as a fraction in lowest terms and calculate the sum of the numerator and denominator.

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