
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
Unit circle \(\Omega\) has points \(X, Y, Z\) on its circumference so that \(X Y Z\) is an equilateral triangle. Let \(W\) be a point other than \(X\) in the plane such that triangle \(W Y Z\) is also equilateral. Determine the area of the region inside triangle \(W Y Z\) that lies outside circle \(\Omega\).

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