
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 $\angle AOB=90^\circ.$ $OY$ is drawn perpendicular to $AB$ and intersects $AB$ at $X.$ Given that the radius $OA = 12$, determine the length of $OY.$ 
[asy]
draw((0,0)--(12,0),black+linewidth(1));
draw((0,0)--(12,12)--(12,0)--cycle,black+linewidth(1));
draw((12,12)--(12,0),black+linewidth(1));
label("$O$",(0,0),SW);
label("$A$",(12,12),N);
label("$B$",(12,0),SE);
label("$X$",(12,6),E);
label("$Y$",(12,0),S);
[/asy]

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