
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

A thin rigid ring with a radius \( R \) is spun around an axis perpendicular to the plane of the ring and passing through its center, attaining an angular velocity \( \omega \). The ring is then placed in a dihedral angle formed by perpendicular planes (horizontal and vertical). The axis of rotation is parallel to the edge of the dihedral angle. The coefficient of friction between the walls of the angle and the ring is \( \mu \). How many rotations will the ring make before it stops?

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