
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 Thomas run on a circular track. Sarah runs counterclockwise, completing a lap every 100 seconds, and Thomas runs clockwise, completing a lap every 75 seconds. They both start from the same line at the same time. At a random time between 12 minutes and 14 minutes after they begin to run, a photographer standing inside the track takes a picture covering one-third of the track, centered on the starting line. What is the probability that both Sarah and Thomas are in the picture?
A) \(\frac{1}{3}\)
B) \(\frac{125}{300}\)
C) \(\frac{111}{200}\)
D) \(\frac{56}{125}\)

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