
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 with centers at (3, -2) and (15, 8) have radii of 3 and 8, respectively. The equation of a common external tangent to these circles can be written in the form \( y = mx + b \) with \( m > 0 \). Find the value of \( b \).
A) \( \frac{719}{11} \)
B) \( \frac{720}{11} \)
C) \( \frac{721}{11} \)
D) \( \frac{722}{11} \)
E) \( \frac{723}{11} \)

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