
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 are drawn on a plane with centers at $O_{1}$ and $O_{2}$ such that each circle passes through the center of the other. $A$ and $B$ are the two points of their intersection. Find the radius of the circles given that the area of the quadrilateral $O_{1} A O_{2} B$ is $2 \sqrt{3}$.

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