
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
Find the smallest sum of distances from an arbitrary point on the plane to the vertices of a unit square.

A problem of the shortest connection for four points. Four points: \(A, B, C,\) and \(D\) are the vertices of a square with side length 1. How should these points be connected by roads to ensure that it is possible to travel from any point to any other and that the sum of the lengths of the roads is minimized? What will be the total length of the roads in this case?

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