
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 Ryan run on a circular track. Rachel runs counterclockwise and completes a lap every 100 seconds, and Ryan runs clockwise and completes a lap every 75 seconds. Both start from the same line at the same time. Between 10 minutes and 11 minutes after they begin to run, a photographer standing inside the track takes a picture at exactly 10 minutes and 30 seconds that shows one-third of the track, centered on the starting line. What is the probability that both Rachel and Ryan are in the picture?
A) $\frac{1}{4}$
B) $\frac{1}{2}$
C) $\frac{3}{4}$
D) $1$

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