
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
Let \( C \) be the circle of radius 12 centered at \((0,0)\). What is the length of the shortest path in the plane between \((8 \sqrt{3}, 0)\) and \((0, 12 \sqrt{2})\) that does not pass through the interior of \( C \)?

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