
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 a plane, a right angle is given. A circle with a center located outside of this angle is tangent to the bisector of the right angle. It intersects one side of the right angle at points \(A\) and \(B\) and the extension of the other side at points \(C\) and \(D\). Given that \(AB = \sqrt{7}\) and \(CD = 1\), find the radius of the circle.

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