
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 the diagram below, point  $A$  lies on the circle centered at  $O$ .  $AB$  is tangent to circle  $O$  with  $\overline{AB} = 6$ . Point  $C$  is  $\frac{2\pi}{3}$  radians away from point  $A$  on the circle, with  $BC$  intersecting circle  $O$  at point  $D$ . The length of  $BD$  is  $3$ . Compute the radius of the circle.

![Image](https://cdn.artofproblemsolving.com/attachments/7/8/baa528c776eb50455f31ae50a3ec28efc291e8.png)

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