
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
Congruent circles  $\Gamma_1$  and  $\Gamma_2$  have radius  $2012,$  and the center of  $\Gamma_1$  lies on  $\Gamma_2.$  Suppose that  $\Gamma_1$  and  $\Gamma_2$   intersect at  $A$  and  $B$ . The line through  $A$  perpendicular to  $AB$  meets  $\Gamma_1$  and  $\Gamma_2$  again at  $C$  and  $D$ , respectively. Find the length of  $CD$ .

*Author: Ray Li*

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