
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 $s$, semicircle arcs with radii $s/2$ and centers at midpoints of $AB$ and $BC$ intersect inside the square. Where they intersect, point $X$ is formed. Calculate how far point $X$ is from the side $AD$.
A) $\frac{s}{4}$  
B) $\frac{s}{2}$  
C) $\frac{3s}{4}$  
D) $\frac{s}{3}$  
E) $\frac{s}{8}$

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