
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
Three circles with centers at \((2, 4)\), \((14, 9)\), and \((8, 16)\) have radii of \(4\), \(9\), and \(6\), respectively. A common external tangent to the first two circles can be written in the form \(y = mx + b\) with \(m > 0\). Determine the value of \(b\).
A) \(\frac{700}{119}\)
B) \(\frac{710}{119}\)
C) \(\frac{712}{119}\)
D) \(\frac{720}{119}\)
E) \(\frac{730}{119}\)

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