
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 $X.$ The radius $OY$ of the circle is given as 10 units. What is the length of $XY$?

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