
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
In the diagram, points $A$, $B$, $C$, $D$, $E$, $F$, and $G$ lie on a straight line with $AB=BC=CD=DE=EF=FG=3$. Semicircles with diameters $AG$, $AB$, $BC$, $CD$, $DE$, $EF$, and $FG$ are drawn. An additional rectangle with length equal to $AG$ and height equal to the radius of semicircle $AG$ is also drawn, such that its base is on line segment $AG$. What is the area of the shaded region formed by the intersection of the rectangle and the semicircles?

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