
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
A rectangle $ABCD$ contains four small squares within it. Three squares are shaded and have non-overlapping interiors, as shown in the diagram. The side length of each smaller shaded square is $2$ inches. Calculate the area of rectangle $ABCD$.

[asy]
size(150);
pair A = (0,0), D = (6,0), C = (6,4), B = (0,4);
draw(A--B--C--D--cycle);
draw(A--(2,0)--(2,2)--(0,2)--cycle);
filldraw(B--(2,4)--(2,2)--(0,2)--cycle, gray(0.7), black);
filldraw((2,0)--(4,0)--(4,2)--(2,2)--cycle, gray(0.7), black);
filldraw((4,0)--(6,0)--(6,2)--(4,2)--cycle, gray(0.7), black);
label("$A$",A,WSW);
label("$B$",B,WNW);
label("$C$",C,ENE);
label("$D$",D,ESE);
[/asy]

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