
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
On the sides of a square, equilateral triangles are constructed externally, and their vertices are subsequently connected. Determine the ratio of the perimeter of the resulting quadrilateral to the perimeter of the given square.

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