
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
What percent of square $PQRS$ is shaded? All angles in the diagram are right angles. The side length of square $PQRS$ is 6 units. There are three shaded rectangles inside the square:
1. The first rectangle starts from the bottom left corner $(0,0)$ to $(2,2)$.
2. The second rectangle starts from $(3,0)$ to $(5,5)$.
3. The third rectangle starts from $(6,0)$ to $(0,6)$.
\[ 
\text{[asy]}
import graph;
defaultpen(linewidth(0.7));

xaxis(0,7,Ticks(1.0,NoZero));
yaxis(0,7,Ticks(1.0,NoZero));

fill((0,0)--(2,0)--(2,2)--(0,2)--cycle);
fill((3,0)--(5,0)--(5,5)--(0,5)--(0,3)--(3,3)--cycle);
fill((6,0)--(7,0)--(7,6)--(0,6)--(0,6)--(6,6)--cycle);

label("$P$",(0,0),SW);
label("$Q$",(0,6),N);
label("$R$",(6,6),NE);
label("$S$",(6,0),E);
\text{[/asy]}
\]

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