
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 a combination of a right triangle and 12 congruent squares arranged in a grid. The hypotenuse PQ of the right triangle, which is also one side of the rectangle forming the complete grid, is 10 cm. If the right triangle's other two sides are of equal length, calculate the total area of the shaded region.

[asy]
for(int i = 0; i < 4; ++i)
{
    for(int j = 0; j < 3; ++j)
    {
        filldraw((i,j)--(i+1,j)--(i+1,j+1)--(i,j+1)--(i,j)--cycle,gray,linewidth(2));
    }
}
draw((0,3)--(3,0)--(3,3)--(0,3)--cycle,linewidth(2));
label("P", (0,3), NW);
label("Q", (3,0), SE);
[/asy]

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