
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
Consider an isosceles triangle $ABC$ where $AB = AC = 2$ and base $BC = 2\sqrt{2}$. Segment $AB$ is also a diameter of a circle with radius $1$. The circle intersects sides $AC$ and $BC$ at points $D$ and $E$ respectively. Find the length of $AE$.
**A)** $1$  
**B)** $1.5$  
**C)** $\sqrt{2}$  
**D)** $2$  
**E)** $2\sqrt{2}$

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