
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 $XYZ$, $XY = 6$, $YZ = 8$, and $ZX = 10$.

[asy]
defaultpen(1);

pair Z=(0,0), X = (0,6), Y = (8,0);
draw(X--Y--Z--cycle);

label("\(X\)",X,N);
label("\(Y\)",Y,E);
label("\(Z\)",Z,SW);
[/asy]

Point $Q$ is randomly selected inside triangle $XYZ$.  What is the probability that $Q$ is closer to $Z$ (vertex with the right angle) than it is to either $X$ or $Y$?

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