
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
Given two concentric circles where the smaller circle has a radius $s$ and the larger circle has a radius $S$. The area of the larger circle is $3/2$ times the area of the space between the two circles. Calculate the ratio of their radii, $S:s$.
A) 2
B) $\sqrt{3}$
C) 3/2
D) 3
E) $\frac{3}{\sqrt{2}}$

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