
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, two pairs of identical right-angled triangles are cut off of rectangle $ABCD$ ($AB=2CD$), leaving another smaller rectangle $PQRS$. Each triangle has one angle at vertex $A$, $B$, $C$, and $D$ respectively. The total area cut off is $300 \text{ m}^2$. Calculate the length of $PR$, in meters. 

[asy]
size(5cm);

pair a = (0, 2); 
pair b = (1, 2); 
pair c = (1, 0); 
pair d = (0, 0);
pair s = (0, 0.5); 
pair p = (0.5, 2); 
pair q = (1, 1.5); 
pair r = (0.5, 0);

// Thicken pen
defaultpen(linewidth(1));

// Fill triangles
path tri1 = a--p--s--cycle;
path tri2 = p--q--b--cycle;
path tri3 = q--c--r--cycle;
path tri4 = s--r--d--cycle;
fill(tri1, gray(0.75));fill(tri2, gray(0.75));
fill(tri3, gray(0.75));fill(tri4, gray(0.75));

// Draw rectangles
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