
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 center $C$ and radius 10 units, and a point \(R\) located 15 units away from $C$, are given. What is the locus of the midpoint of the segment connecting \(R\) to a point \(S\) as \(S\) varies along the circumference of the circle?
A) Circle with center (0,7.5) and radius 5 units
B) Circle with center (0,10) and radius 3.3 units
C) Circle with center (0,20) and radius 5 units
D) Circle with center (0,15) and radius 3.3 units

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