
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
What is the area of the letter  $O$  made by Dürer? The two circles have a unit radius. Their centers, or the angle of a triangle formed by an intersection point of the circles is  $30^o$ .
![Image](https://cdn.artofproblemsolving.com/attachments/b/c/fe052393871a600fc262bd60047433972ae1be.png)

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