
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
Consider a large rectangle $ABCD$. Inside this rectangle are positioned two squares and a right triangle. The area of the shaded square on the bottom left corner is 4 square inches. The second square, on the left side with a common side with the shaded square, has the same side length. Above both squares, there's a right triangle $XYZ$ where $X$ is a point on the top left, $Y$ is along the top of the square on the left, and $Z$ is positioned directly above the upper right corner of the shaded square. Determine the area of rectangle $ABCD$ in square inches if the height of triangle $XYZ$ from $XZ$ to $Y$ is equal to the side of the shaded square.

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