
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
Square $PQRS$ is inscribed in right triangle $XYZ$, as shown below. If $XY = 35$ units and $YZ = 75$ units, what is the area of square $PQRS$?

[asy]
draw((9,15.6)--(10.7,14.6)--(11.7,16.3));
draw((0,0)--(15,25.5)--(75,0)--cycle);
draw((0,15.5)--(0,0)--(15.5,0)--(15.5,15.5)--cycle);
label("$X$",(0,0),SW);
label("$P$",(0,15.5),W);
label("$Q$",(15.5,15.5),N);
label("$R$",(15.5,0),S);
label("$S$",(0,0),S);
label("$Y$",(15,25.5),N);
label("$Z$",(75,0),SE);
[/asy]

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