
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 $\omega_{1}$ and $\omega_{2}$ with equal radius $R$ intersect such that the center of one circle lies outside the other. Let the center of $\omega_{1}$ be denoted by $O_{1}$ and the center of $\omega_{2}$ by $O_{2}$. Let $B$ be one of the intersection points of the circles. The line $O_{1}B$ intersects the circle $\omega_{2}$ again at point $C$ such that $O_{2}C$ is perpendicular to $O_{1}O_{2}$. Find the distance between the centers of the circles.

Answer: $R \sqrt{3}$.

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