
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
A line segment $\overline{AB}$ is divided at point $C$ such that $AC = 4CB$. Circles are described with $\overline{AC}$ and $\overline{CB}$ as diameters. A common tangent to these circles touches AB extended at $D$. Determine the length of $BD$ in terms of $CB$.
A) $5x$
B) $4x$
C) $x$
D) $\frac{x}{2}$
E) $\frac{x}{4}$

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