
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 triangle $XYZ$, $\angle YXZ$ is a right angle, with $m\angle XYZ = 60^\circ$, and $XY = 16$. Let $P$ be randomly chosen inside $XYZ$, and extend $\overline{YP}$ to meet $\overline{XZ}$ at $Q$. What is the probability that $YQ > 8\sqrt{2}$?
A) $\frac{2-\sqrt{2}}{2}$
B) $\frac{1}{3}$
C) $\frac{3-\sqrt{3}}{3}$
D) $\frac{1}{2}$
E) $\frac{5-\sqrt5}{5}$

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