
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 the diagram, four isosceles right triangles are cut off a square $ABCD$, leaving rectangle $PQRS$. Two triangles from adjacent sides are merged into a larger isosceles right triangle, and the total area cut off is $400 \text{ m}^2$. What is the length of $PR$, in meters?
[asy]
size(5cm);

pair a = (0, 1); pair b = (1, 1); pair c = (1, 0); pair d = (0, 0);
pair s = (0, 0.500); pair p = (0.500, 1); pair q = (1, 0.500); pair r = (0.500, 0);

defaultpen(linewidth(1));

// Fill triangles
path tri1 = a--p--s--cycle;
path tri12 = s--r--d--cycle;
path tri2 = p--q--b--cycle;
path tri3 = q--c--r--cycle;

fill(tri1, gray(0.75)); fill(tri12, gray(0.75));
fill(tri2, gray(0.75)); fill(tri3, gray(0.75));

// Draw rectangles and triangles
draw(a--b--c--d--cycle); draw(p--q--r--s--cycle);

// Labels
label("$A$", a, NW); label("$B$", b, NE); label("$C$", c, SE); label("$D$", d, SW);
label("$P$", p, N); label("$Q$", q, E); label("$R$", r, S); label("$S$", s, W);

[/asy]

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