
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
Side \( AB \) of triangle \( ABC \) is a chord of a circle. The sides \( AC \) and \( BC \) lie within the circle. The extension of side \( AC \) intersects the circle at point \( D \), and the extension of side \( BC \) intersects the circle at point \( E \). Given that \( AB = AC = CD = 2 \) and \( CE = \sqrt{2} \), find the radius of the circle.

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