
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
The angle XYZ is a right angle. The three quadrilaterals shown are squares. The sum of the areas of the three squares is 450 square centimeters. Additionally, the side length of square on XY is 5 cm less than side length of square on YZ. What is the number of square centimeters in the area of the largest square?

[asy]
draw((0,0)--(15,0)--(0,8)--cycle);
dot((0,0));
dot((15,0));
dot((0,8));
draw((0,0)--(0,8)--(-8,8)--(-8,0)--cycle);
draw((0,0)--(0,-15)--(15,-15)--(15,0));
draw((0,8)--(8,23)--(23,15)--(15,0)--cycle);
label("$X$",(0,8),NW);
label("$Y$",(0,0),SE);
label("$Z$",(15,0),E);
[/asy]

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