
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
Given a line segment $\overline{AB}$, point $C$ divides $\overline{AB}$ such that $AC = 2CB$. Circles are drawn with $\overline{AC}$ and $\overline{CB}$ as diameters. A common external tangent to these circles extends and meets the extension of $\overline{AB}$ at point $D$, where $D$ is on the extension of $AB$ beyond $B$. Find the length of $BD$ in terms of $CB$.

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