
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 shaded region consists of 20 congruent squares arranged as follows: 10 squares form a rectangular strip and the rest form two smaller squares, each aligning perfectly beside the rectangular strip. If $PQ = 8$ cm, where $PQ$ is the diagonal of a square formed by 16 of these shaded squares, what is the area of the entire shaded region?

[asy]
for(int i = 0; i < 6; ++i) {
  for(int j = 0; j < 2; ++j) {
    filldraw((i,j)--(i+1,j)--(i+1,j+1)--(i,j+1)--(i,j)--cycle,gray,linewidth(2));
  }
}

for(int i = 0; i < 2; ++i) {
  for(int j = 2; j < 4; ++j) {
    filldraw((i,j)--(i+1,j)--(i+1,j+1)--(i,j+1)--(i,j)--cycle,gray,linewidth(2));
    filldraw((j,i)--(j+1,i)--(j+1,i+1)--(j,i+1)--(j,i)--cycle,gray,linewidth(2));
  }
}

draw((3,0)--(4,0)--(4,4)--(0,4)--(0,3)--cycle,linewidth(2));

label("P",(0,4),NW);
label("Q",(4,0),SE);
[/asy]

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