
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
Alice and Bob are walking in the same direction, Bob at 4 feet per second and Alice at 2 feet per second, on parallel paths that are 300 feet apart. A large circular monument 150 feet in diameter is centered midway between the paths. When the monument first blocks the line of sight between Alice and Bob, they are 300 feet apart. Determine the amount of time, $t$, in seconds, until Alice and Bob can see each other again. Provide $t$ 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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