
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
A circle with its center located inside a right angle is tangent to one side of the angle, intersects the other side at points $A$ and $B$, and intersects the angle bisector at points $C$ and $D$. Given that $AB = \sqrt{6}$ and $CD = \sqrt{7}$, find the radius of the circle.

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