
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 in a 'T' shape. If $PQ = 8$ cm, where $PQ$ is the diagonal intersecting four squares within this arrangement, calculate the total area of the shaded region.
[asy]
for(int i = 0; i < 5; ++i)
{
    for(int j = 0; j < 4; ++j)
    {
        if ((i < 2 || j == 1))
        {
            filldraw((i,j)--(i+1,j)--(i+1,j+1)--(i,j+1)--cycle,gray,linewidth(2));
        }
    }
}
draw((1,3)--(3,3)--(1,1)--cycle,linewidth(2));
label("P",(1,3),N);
label("Q",(3,3),E);
[/asy]

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