
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
The points  $A,B,$  and  $C$  lies on the circumference of the unit circle. Furthermore, it is known that  $AB$  is a diameter of the circle and \[\frac{|AC|}{|CB|}=\frac{3}{4}.\] The bisector of  $ABC$  intersects the circumference at the point  $D$ . Determine the length of the  $AD$ .

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