
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
In the xy-plane, what is the length of the shortest path from $(0,0)$ to $(15,20)$ that does not go inside the circle $(x-7.5)^{2} + (y-10)^{2} = 36$?
A) $20 + 2\pi$
B) $20\sqrt{\frac{120.25}{900}} + 2\pi$
C) $20\sqrt{3} + \frac{6\pi}{3}$
D) $25 + 2\pi$
E) $30\sqrt{3} + 3\pi$

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