
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 square $ABCD$ with side length $s$, three quarter-circle arcs are drawn with the first arc centered at $A$ with radius $s$ covering the region towards $B$, the second arc centered at $B$ with radius $s$ covering the region towards $A$, and the third arc centered at $C$ with radius $s$ covering the region towards $D$, where these arcs intersect at one point inside the square, calculate the distance from this intersection point to side $AB$.

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