
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
In square $ABCD$ with side length $s$, quarter-circle arcs with radii $s$ are drawn with centers at corners $A$ and $D$. These arcs intersect at a new point $X$ inside the square. Determine the distance from $X$ to the side $BC$ of the square.
A) $s$
B) $\frac{s\sqrt{3}}{2}$
C) $\frac{s}{2}$
D) $\frac{s(1+\sqrt{3})}{2}$
E) $\frac{s(2-\sqrt{3})}{2}$

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