
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
ABCD is a rectangle. AEB is isosceles with E on the opposite side of AB to C and D and lies on the circle through A, B, C, D. This circle has radius 1. For what values of |AD| do the rectangle and triangle have the same area?

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