
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 100 seconds, and Robert runs clockwise and completes a lap every 70 seconds. Both start from the same line at the same time. Between 12 minutes and 13 minutes after they begin to run, a photographer standing inside the track takes a picture that shows one-fifth of the track, centered on the starting line. What is the probability that both Rachel and Robert are in the picture?
A) $\frac{1}{20}$
B) $\frac{1}{18}$
C) $\frac{1}{16}$
D) $\frac{1}{14}$
E) $\frac{1}{12}$

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