
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 sphere with a radius of 4 and two points \( A \) and \( B \) on its surface, where \( AB = 4\sqrt{2} \), and the center of the sphere is \( O \). If a moving point \( C \) on the sphere satisfies that the dihedral angle \( C-AB-O \) is \( 60^\circ \), find the radius of the circumscribed sphere of the tetrahedron \( OABC \).

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