
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
The shaded design shown in the diagram is made by drawing eight circular arcs, all with the same radius. The centers of four arcs are the vertices of the square; the centers of the four touching arcs are the midpoints of the sides of the square. The diagonals of the square have length 1. Calculate the total length of the border of the shaded design.

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