
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 race on a circular track. Rachel runs counterclockwise, completing a lap every 120 seconds, while Robert runs clockwise, completing a lap every 100 seconds. They start simultaneously from the same line. Between 15 minutes and 20 minutes after they begin running, a photographer stationed inside the track takes a photo covering one-third of the track, centered on the starting line. What is the probability that both Rachel and Robert are simultaneously captured in the photograph?
A) $\frac{1}{12}$
B) $\frac{1}{10}$
C) $\frac{1}{9}$
D) $\frac{1}{8}$

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