
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 $A$, $B$, $C$, $D$, $E$, and $F$ lie on a straight line with $AB=3$, $BC=CD=DE=4$, $EF=5$. Semicircles with diameters $AF$, $AB$, $BC$, $CD$, $DE$, and $EF$ form a shape as shown. What is the area of the shaded region?
[asy]
size(6cm); defaultpen(fontsize(9));
pair a = (0, 0); pair b = a + 3*right; pair c = b + 4*right; pair d = c + 4*right; pair e = d + 4*right; pair f = e + 5*right;
path region = a{up}..{down}f..{up}e..{down}d..{up}c..{down}b..{up}a--cycle;
filldraw(region, gray(0.75), linewidth(0.75));
draw(a--f, dashed + linewidth(0.75));
label("$A$", a, W); label("$F$", f, E);
label("$B$", b, 1.5 * SE); label("$D$", d, 1.5 * SE);
label("$C$", c, 1.5 * SW); label("$E$", e, 1.5 * SW);
[/asy]

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