
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
Three coplanar squares with side lengths of three, five, and seven units, respectively, are arranged side-by-side so that one side of each square lies on line $CD$. A segment connects the bottom left corner of the smallest square to the upper right corner of the largest square. Determine the area of the shaded quadrilateral formed between line $CD$, the bottom side of the smallest square, and the segment connecting the corners as described. [asy] size(150); defaultpen(linewidth(0.9)+fontsize(10));
fill((3,0)--(8,0)--(8,4.5)--(3,1.5)--cycle,gray(0.8));
draw(scale(3)*unitsquare);
draw(shift(3,0)*scale(5)*unitsquare);
draw(shift(8,0)*scale(7)*unitsquare);
draw((0,0)--(15,7.5));

real d = 1.2; pair d2 = (0.9,0);
pair C = (-d,0), D = (15+d,0); dot(C,linewidth(3)); dot(D,linewidth(3)); label("C",C,(0,-1.5)); label("D",D,(0,-1.5));
label("3",(1.5,3.7)); label("5",(5.5,5.7)); label("7",(11.5,7.7));
[/asy]

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