
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
A set of straight line segments either inside or on the border of a square with side length 1 is called "opaque" if any straight line intersecting the square intersects at least one of these segments. For example, two diagonals form an opaque set. The total length of the diagonals is \(2 \sqrt{2} \approx 2.82\). It is fairly easy to show through elementary calculations that the minimum sum of the lengths of the segments of an opaque symmetric set is approximately \(1 + \gamma \overline{3} \approx 2.73\). Find an opaque set with a total length of segments less than \(1 + \sqrt{3}\).

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