
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
Inside square $ABCD$ with side $s$, a quarter-circle arc with radius $s$ centered at $A$, and another quarter-circle arc with radius $\frac{s}{2}$ centered at $D$ are drawn. These arcs intersect at a point $Y$ inside the square. Find the distance from $Y$ to the side $CD$.
A) $\frac{s}{6}$
B) $\frac{s}{8}$
C) $\frac{s}{4}$
D) $\frac{s}{10}$

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