
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 a circle and a square centered at the origin in a coordinate system, where the circle and square are concentric and each vertex of the square touches the circle. If the equation of the circle is \(x^2 + y^2 = r^2\) and the side length of the square is \(s\), find the relationship between \(r\) and \(s\) such that these geometric conditions are satisfied.
A) \(r = \frac{s}{\sqrt{2}}\)
B) \(r = \frac{s\sqrt{2}}{2}\)
C) \(r = s\)
D) \(r = 2s\)

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