
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
Consider a circle in which a square is inscribed. Within this square, an equilateral triangle is inscribed, such that one side of the triangle coincides with the top side of the square. Determine the ratio of the area of the equilateral triangle to the area of the inscribed square.

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