
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 $PQRS$ with side $t$, quarter-circle arcs with radii $t$ and centers at $P$ and $Q$ are drawn. These arcs intersect at a point $Y$ inside the square. How far is $Y$ from the side $RS$?
A) $\frac{t}{2}$
B) $\frac{t \sqrt{3}}{2}$
C) $\frac{t(2 - \sqrt{3})}{2}$
D) $\frac{t(\sqrt{3}+1)}{2}$

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