
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
Four coplanar squares with sides of lengths three, five, seven, and nine units, respectively, are arranged side-by-side so that one side of each square lies on line $AB$, and a segment connects the bottom left corner of the smallest square to the upper right corner of the largest square. What is the area of the shaded quadrilateral? [asy] size(200); defaultpen(linewidth(0.9)+fontsize(10));
fill((3,0)--(15,0)--(15,4.5)--(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(shift(15,0)*scale(9)*unitsquare);
draw((0,0)--(24,9));

real d = 1.5; pair d2 = (1.2,0);
pair A = (-d,0), B = (24+d,0); dot(A,linewidth(3)); dot(B,linewidth(3)); label("A",A,(0,-1.5)); label("B",B,(0,-1.5)); draw(A-d2--B+d2,Arrows(4));
label("3",(1.5,3.8)); label("5",(5.5,5.5)); label("7",(11.5,7.6)); label("9",(19.5,9.8));
[/asy]

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