
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
Given a tetrahedron $A-BCD$ where $AB=CD= \sqrt {2}$, $AC=BC=AD=BD= \sqrt {3}$, and all vertices are on the same sphere, find the radius of the sphere and use this information to calculate the volume of the sphere.

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