
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
Given Triangle $XYZ$ is a right triangle with $\angle YXZ$ as its right angle, $\angle XYZ = 30^\circ$ and $XY = 12$. A point $Q$ is randomly selected within $XYZ$, and extend $\overline{YQ}$ to meet $\overline{XZ}$ at $W$. Find the probability that the length of $YW > 6\sqrt{3}$.

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