
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
The following construction is used for training astronauts:
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  $2$ . The 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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