
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 externally tangent circles with centers at points $A$ and $B$ have radii of lengths $7$ and $4$, respectively. A line externally tangent to both circles intersects ray $AB$ at point $C$. What is the length of $BC$?
A) $\frac{40}{3}$
B) $\frac{44}{3}$
C) $\frac{48}{3}$
D) $\frac{52}{3}$

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