
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
$ABCD$ is a rectangle whose area is 18 square units. $E$ and $F$ are points on $AD$ and $BC$, respectively, such that $AE=2$ units and $BF=3$ units. A new point $G$ is positioned above $EF$ such that triangle $EFG$ is isosceles with $EG=FG$. Calculate the area of trapezoid $ABFE$ and triangle $EFG$ combined.

[asy]
size(4cm,4cm);
pair A=(0,0), B=(6,0), C=(6,3), D=(0,3), E=(2,0), F=(4,3), G=(3,3.5);
draw(A--B--C--D--cycle);
draw(E--F--G--cycle);
draw(A--E);
draw(B--F);
filldraw(E--F--G--cycle, lightgray);
filldraw(A--B--F--E--cycle, lightblue);
label("$A$", A, SW);
label("$B$", B, SE);
label("$C$", C, NE);
label("$D$", D, NW);
label("$E$", E, S);
label("$F$", F, N);
label("$G$", G, N);
[/asy]

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