
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 diagram shows three rectangles with non-overlapping interiors. The area of the shaded rectangle is 2 square inches, and it is twice as long as it is wide. What is the area of the larger rectangle $EFGH$, in square inches?

[asy]size(100);
pair E = (0,0), H = (5,0),G = (5,3),F = (0,3);
draw(E--F--G--H--cycle);
draw(E--(2,0)--(2,1)--(0,1)--cycle);
filldraw(F--(2,3)--(2,1)--(0,1)--cycle,gray(.6),black);
label("$E$",E,WSW);
label("$F$",F,WNW);
label("$G$",G,ENE);
label("$H$",H,ESE);[/asy]

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