
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 coordinate plane ( \(x, y\) ), there is a circle with radius 4 centered at the origin. A line given by the equation \( y = \sqrt{3} x - 4 \) intersects the circle at points \( A \) and \( B \). Find the sum of the length of segment \( AB \) and the length of the larger arc \( AB \).

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