
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 all possible tetrahedra \( A B C D \) where \( A B = 4 \), \( A C = C B = 5 \), and \( A D = D B = 6 \). We inscribe each of these tetrahedra in a cylinder such that all vertices lie on the lateral surface of the cylinder and the edge \( C D \) is parallel to the axis of the cylinder. Choose the tetrahedron for which the cylinder's radius is the smallest among the ones obtained. What values can the length of \( C D \) take in such a tetrahedron?

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