
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 right triangle $XYZ$ with the leg $XZ$ as the diameter, a circle is constructed that intersects the hypotenuse $XY$ at point $W$. A tangent is drawn through point $W$ to the circle, which intersects the leg $ZY$ at point $V$. Find the length of $VY$, given that $XW = 12$ and $YW = 4$.

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