
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
Sarah and John run on a circular track. Sarah runs counterclockwise and completes a lap every 120 seconds, while John runs clockwise and completes a lap every 75 seconds. Both start from the same line at the same time. A photographer standing inside the track takes a picture at a random time between 15 minutes and 16 minutes after they begin to run. The picture shows one-third of the track, centered on the starting line. What is the probability that both Sarah and John are in the picture?
A) $\frac{1}{24}$
B) $\frac{1}{16}$
C) $\frac{1}{12}$
D) $\frac{1}{8}$
E) $\frac{1}{6}$

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