
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  $ABC$  be a triangle with  $AB = 4024$ ,  $AC = 4024$ , and  $BC=2012$ . The reflection of line  $AC$  over line  $AB$  meets the circumcircle of  $\triangle{ABC}$  at a point  $D\ne A$ . Find the length of segment  $CD$ .

*Ray Li.*

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