
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 with centers at points $A$ and $B$ are externally tangent to each other, with radii $6$ and $4$ respectively. A line that is tangent to both circles at different points intersects the ray $AB$ at point $C$. Find the length of segment $BC$.
A) 16
B) 18
C) 20
D) 22
E) 24

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