
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 swimmers do their training in a rectangular quarry. The first swimmer finds it convenient to start at one corner of the quarry, so he swims along the diagonal to the opposite corner and back. The second swimmer finds it convenient to start from a point that divides one of the sides of the quarry in the ratio \(2018:2019\). He swims around a quadrilateral, visiting one point on each shore, and returns to the starting point. Can the second swimmer select points on the three other shores in such a way that his path is shorter than that of the first swimmer? What is the minimum value that the ratio of the length of the longer path to the shorter path can take?

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