
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
On a coordinate plane ( $x ; y$ ), a circle with a radius of 4 is 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 $A B$ and the length of the larger arc $A B$.

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