
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
Circle $X$ has radius $144$. Circle $Y$, with an integer radius $s < 144$, rolls internally tangent to circle $X$. It completes one full rotation around Circle $X$, returning to its initial tangency point without slipping. How many possible values can $s$ have given that at no point does the circle $Y$ cease to be tangent to circle $X$?
A) 9  
B) 12  
C) 14  
D) 15  
E) 18

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