
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 circle \( C_{2} \) of radius \( 2R \) rolls along the inside of another, fixed circle \( C_{1} \) of radius \( nR \), where \( n \) is an integer greater than 2. An astronaut is fastened to a third circle \( C_{3} \) of radius \( R \) which rolls along the inside of circle \( C_{2} \) in such a way that the touching point of the circles \( C_{2} \) and \( C_{3} \) remains at maximum distance from the touching point of the circles \( C_{1} \) and \( C_{2} \) at all times.

How many revolutions (relative to the ground) does the astronaut perform together with the circle \( C_{3} \) while the circle \( C_{2} \) completes one full lap around the inside of circle \( C_{1} \)?

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