
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 $AB=BC=5$, $CD=DE=10$, and $EF=FG=5$. Semicircles with diameters $AG$, $AB$, $BC$, $CD$, $DE$, $EF$, and $FG$ create the shape shown in the diagram below. Calculate the area of the shaded region formed by the overlapping semicircles.
[asy]
size(8cm); defaultpen(fontsize(10));
pair one = (2, 0);
pair a = (0, 0); pair b = a + one; pair c = b + one; pair d = c + 2*one; pair e = d + 2*one; pair f = e + one; pair g = f + one;
path region = a{up}..{down}g..{up}f..{down}e..{up}d..{down}c..{up}b..{up}a--cycle;
filldraw(region, gray(0.75), linewidth(0.75));
draw(a--g, dashed + linewidth(1));

// labels
label("$A$", a, S); label("$G$", g, S);
label("$B$", b, 1 * N); label("$F$", f, 1 * N);
label("$C$", c, 1 * S); label("$E$", e, 1 * S);
label("$D$", d, 2 * N);
[/asy]

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