
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
Two circles with centers  $A$  and  $B$  intersect at points  $X$  and  $Y$ . The minor arc  $\angle{XY}=120$  degrees with respect to circle  $A$ , and  $\angle{XY}=60$  degrees with respect to circle  $B$ . If  $XY=2$ , find the area shared by the two circles.

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