
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 run on a circular track. Rachel runs counterclockwise and completes a lap every 80 seconds, while Robert runs clockwise and completes a lap every 100 seconds. They start from the same line at the same time. Between 5 and 6 minutes after starting their run, a photographer standing outside the track takes a picture covering one-third of the track, centered on the starting line. What is the probability that both Rachel and Robert appear in the picture at the same time?
A) $\frac{4}{9}$
B) $\frac{5}{9}$
C) $\frac{6}{9}$
D) $\frac{7}{9}$

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