
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 with radius 150 (circle A) has a smaller circle with radius r (circle B) rolling inside it. Circle B starts at one point of tangency and must end at another point of tangency after one complete revolution inside circle A, without slipping. Given that the radius r of circle B is less than 150, find how many integer values r can be.
A) 10
B) 11 
C) 12 
D) 24 
E) 30

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