
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
In triangle  $ABC$ ,  $AB = 28$ ,  $AC = 36$ , and  $BC = 32$ . Let  $D$  be the point on segment  $BC$  satisfying  $\angle BAD = \angle DAC$ , and let  $E$  be the unique point such that  $DE \parallel AB$  and line  $AE$  is tangent to the circumcircle of  $ABC$ . Find the length of segment  $AE$ .

*Ray Li*

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