
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 a unit circle, draw the diameter \(AC\), and let \(B\) be the point on the arc \(AC\) such that \(\angle BOA = 30^\circ\) (where \(O\) is the center of the circle). The tangent at \(A\) intersects the line \(CB\) at \(D\). What is the difference between the length of the arc \(AB\) and the segment \(AD\)?

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