
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
In a given diagram, there are three circles of radius 3 units, each having a central angle of 90 degrees. They are arranged such that their centers form an equilateral triangle and each circle intersects exactly at one point with each of the other two circles at their respective points of tangency. Calculate the area of the region enclosed by these arcs.

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