
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, $COB$ is a sector of a circle with $\angle COB=90^\circ.$ $OZ$ is drawn perpendicular to $CB$ and intersects $CB$ at $X.$ What is the length of $XZ$? Assume the radius $OC=CB=15.$ 
[asy]
draw((0,0)--(15,0),black+linewidth(1));
draw((0,0)--(15,-15),black+linewidth(1));
draw((15,0)--(15,-15),black+linewidth(1));
label("$O$",(0,0),W);
label("$C$",(15,-15),S);
label("$B$",(15,0),E);
label("$X$",(15,-7.5),E);
label("$Z$",(15,0),NE);
label("15",(0,0)--(15,-15),SW);
label("15",(0,0)--(15,0),NW);
[/asy]

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