
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
Circles $A$, $B$, and $C$ are externally tangent to each other and internally tangent to a larger circle $D$. Circles $B$ and $C$ are congruent. Suppose circle $A$ has radius 2 and the center of circle $D$ is on circle $A$, and the radius of circle $D$ is twice the diameter of $A$. What is the radius of circle $B$?

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