
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 square with vertices at coordinates $(0,0)$, $(0,s)$, $(s,0)$, and $(s,s)$, find the locus of all points $P(x,y)$ in the plane such that the sum of the squares of the distances from $P$ to each vertex is $4s^2$.
A) A circle of radius $s/\sqrt{2}$
B) A circle of radius $s/2$
C) A circle of radius $s$
D) Four isolated points
E) None of these

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