
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 \(ABCD\) where \(AB = 4\), \(AC = CB = 7\), and \(AD = DB = 8\). Each of these tetrahedra is inscribed in a cylinder in such a way that all vertices lie on the lateral surface, and the edge \(CD\) is parallel to the axis of the cylinder. Choose the tetrahedron for which the radius of the cylinder is the smallest of those obtained. What values can the length of \(CD\) take in such a tetrahedron?

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