
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 $(x-4)^{2}+(y-6)^{2}= 16$?
A) $12 + 6\pi$  
B) $12 + 10\pi$  
C) $12 + 8\cos^{-1}\left(\frac{4}{\sqrt{52}}\right)$  
D) $12$

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