
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  $AD$  be a diameter of a circle of radius  $r,$  and let  $B,C$  be points on the circle such that  $AB=BC=\frac r2$  and  $A\neq C.$  Find the ratio  $\frac{CD}{r}.$ 

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