
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 a circle with radius 10 units, a sector $COD$ is defined with a central angle $\angle COD = 45^\circ$. A line $CZ$ is drawn perpendicular to $CD$ and intersects $CD$ at point $W$. Calculate the length of $WZ$.

![Illustration here: Draw a circle with center O, radius 10, draw sector COD with angle 45 degrees, perpendicular line CZ intersecting CD at W with Z outside the circle.]

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