
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 Reuleaux triangle is a shape formed from an equilateral triangle by adding circular arcs with the centers at the vertices of the triangle and with radii equal to the side of the triangle.

What is the area of a Reuleaux triangle if the equilateral triangle has a side length of \(1 \text{ cm}\)?

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