
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 have centers at $(1,3)$ and $(10,6)$ with radii $3$ and $6$, respectively. Determine the y-intercept of a common external tangent to the circles if the tangent line can be expressed in the form $y=mx+b$ with $m>0$.
A) $\frac{5}{4}$  
B) $\frac{6}{4}$  
C) $\frac{7}{4}$  
D) $\frac{8}{4}$  
E) $\frac{9}{4}$

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