
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

Two persons, A and B, depart simultaneously from points A and B respectively (A departs from A), and travel towards each other without stopping to return between the two points. The speed of A is 4 times that of B. Given that the distance between A and B is S kilometers, where S is a positive integer and has 8 factors. The first time they meet at point C (note: here the meeting can mean a face-to-face encounter or being overtaken from behind), the length AC is an integer; the second time they meet at point D, the length AD is still an integer. After the second meeting, B feels that his speed is too slow, so he borrows a motorcycle from a villager in the nearby village near point D. By the time he returns to point D with the motorcycle, A has reached point E (A hasn't returned to point A yet), and the length AE is an integer. Finally, B rides the motorcycle to chase A, and the speed of the motorcycle is 14 times the speed of A, and both reach point A at the same time. Determine the distance between points A and B in kilometers.

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