
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 the diagram, $AOB$ is a sector of a circle with center $O$ and $\angle AOB=90^\circ$. $OY$ is drawn perpendicular to $AB$ and intersects $AB$ at $X$. Determine the length of $XY$ if the radius of the circle is 10 units. [asy]
draw((0,0)--(10,0),black+linewidth(1));
draw((0,0)--(7.07,-7.07)..(10,0)..(7.07,7.07)--(0,0),black+linewidth(1));
draw((7.07,-7.07)--(7.07,7.07),black+linewidth(1));
label("$O$",(0,0),W);
label("$A$",(7.07,7.07),N);
label("$B$",(7.07,-7.07),S);
label("$X$",(7.07,0),SE);
label("$Y$",(10,0),E);
label("10",(0,0)--(7.07,7.07),NW);
label("10",(0,0)--(7.07,-7.07),SW);
[/asy]

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