
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 tetrahedrons \(A B C D\) where \(A B = 2\), \(A C = C B = 5\), and \(A D = D B = 7\). Each such tetrahedron is inscribed in a cylinder such that all vertices lie on the lateral surface of the cylinder and the edge \(C D\) is parallel to the cylinder's axis. Choose the tetrahedron for which the cylinder's radius is the smallest among the obtained ones. 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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