
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  $O_1$  and  $O_2$  be concentric circles with radii 4 and 6, respectively.  A chord  $AB$  is drawn in  $O_1$  with length  $2$ .  Extend  $AB$  to intersect  $O_2$  in points  $C$  and  $D$ .  Find  $CD$ .

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