
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
Triangle $XYZ$ is a right triangle with $\angle XYZ$ as its right angle, $m\angle YXZ = 60^\circ$, and $XY = 12$. Let $P$ be randomly chosen inside $XYZ$, and extend $\overline{YP}$ to meet $\overline{XZ}$ at $D$. Find the probability that $YD > 6\sqrt{2}$.

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