
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
A point $P$ is randomly placed inside the right triangle $\triangle XYZ$ where $X$ is at $(0,6)$, $Y$ is at $(0,0)$, and $Z$ is at $(9,0)$. What is the probability that the area of triangle $PYZ$ is less than half of the area of triangle $XYZ$?
[asy]
size(7cm);
defaultpen(linewidth(0.7));
pair X=(0,6), Y=(0,0), Z=(9,0), P=(2,2);
draw(X--Y--Z--cycle);
draw(Y--P--Z);
label("$X$",X,NW);
label("$Y$",Y,SW);
label("$Z$",Z,E);
label("$P$",P,N);
draw((0,0.6)--(0.6,0.6)--(0.6,0));[/asy]

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