
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 25 congruent squares. If $PQ = 10$ cm, what is the area of the entire shaded region?

[asy]
for(int i = 0; i < 6; ++i)
{
    for(int j = 0; j < 3; ++j)
    {
        filldraw((i,j)--(i+1,j)--(i+1,j+1)--(i,j+1)--cycle,gray,linewidth(2));
    }
}
for(int i = 0; i < 3; ++i)
{
    for(int j = 0; j < 6; ++j)
    {
        filldraw((i,j)--(i+1,j)--(i+1,j+1)--(i,j+1)--cycle,gray,linewidth(2));
    }
}
draw((3,3)--(6,3)--(3,6)--(3,3)--cycle,linewidth(2));
label("P",(3,6),N);
label("Q",(6,3),E);
[/asy]

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