
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
Xiao Li and Xiao Zhang are running at a constant speed on a circular track. They start from the same point at the same time, with Xiao Li running clockwise, completing a lap every 72 seconds, and Xiao Zhang running counterclockwise, completing a lap every 80 seconds. Given that there is a $\frac{1}{4}$ arc segment of the track defined with the starting point as the center, how many seconds will the two of them simultaneously be within the defined segment from the time they start to the time they both return to the starting point?

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