
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
Emma and Ethan run on a circular track. Emma runs counterclockwise and completes a lap every 120 seconds, and Ethan runs clockwise and completes a lap every 100 seconds. Both start from the same line at the same time. A photographer standing inside the track takes a picture showing one-fifth of the track, centered on the starting line, at some random time between 15 minutes and 16 minutes after they begin running. What is the probability that both Emma and Ethan are in the photograph?
A) $\frac{1}{20}$
B) $\frac{1}{10}$
C) $\frac{1}{5}$
D) $0$

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