
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 that the line segment \(AB\) is the diameter of a sphere \(O\) with a radius of 2, points \(C\) and \(D\) lie on the surface of sphere \(O\), \(CD = 2\), \(AB \perp CD\), and \(45^{\circ} \leq \angle AOC \leq 135^{\circ}\), what is the range of values for the volume of the tetrahedron \(ABCD\)?

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