
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
Rachel and Robert run on a circular track. Rachel runs counterclockwise and completes a lap every 120 seconds, and Robert runs clockwise and completes a lap every 100 seconds. Both start from the same line at the same time. At some random time between 15 minutes and 16 minutes after they begin to run, a photographer standing inside the track takes a picture that shows one-third of the track, centered on the starting line. What is the probability that both Rachel and Robert are in the picture?
A) $\frac{7}{15}$
B) $\frac{23}{30}$
C) $\frac{46.66}{60}$
D) $\frac{31}{60}$
E) $\frac{3}{4}$

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