
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
In a circular stadium, two runners, Anna and Carl, run on the same track. Anna runs counterclockwise, completing a lap every 100 seconds, and Carl jogs clockwise, completing a lap every 60 seconds. They start running from the same point at the same time. A photographer stationed inside the track takes a photo of one-third of the track, centered on the starting line, at a random time between 12 minutes and 15 minutes from the start. Calculate the probability that Anna and Carl are both in the frame of the photo.

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