
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 a linear diagram, points $A$, $B$, $C$, $D$, $E$, $F$, $G$, $H$, and $I$ lie on a straight line with $AB=BC=CD=DE=EF=FG=GH=HI=4$. Semicircles with diameters $AI$, $AB$, $BC$, $CD$, $DE$, $EF$, $FG$, $GH$, and $HI$ are drawn to form a pattern as shown. Calculate the area of the shaded region formed by these semicircles.

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