
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 rectangle $ABCD$, side $AB$ measures $8$ units and side $BC$ measures $4$ units, as shown. Points $F$ and $G$ are on side $CD$ with segment $DF$ measuring $2$ units and segment $GC$ measuring $3$ units, and lines $AF$ and $BG$ intersect at $E$. Determine the area of triangle $AEB$. [asy]
draw((0,0)--(8,0)--(8,4)--(0,4)--cycle);
draw((0,0)--(3,8)--(8,0)--cycle);
dot((0,0));
dot((8,0));
dot((8,4));
dot((0,4));
dot((2,4));
dot((5,4));
dot((3,8));
label("A",(0,0),SW);
label("B",(8,0),SE);
label("C",(8,4),NE);
label("D",(0,4),NW);
label("E",(3,8),N);
label("F",(2,4),SE);
label("G",(5,4),SW);
label("8",(4,0),S);
label("2",(1,4),N);
label("3",(6.5,4),N);
label("4",(8,2),E);
[/asy]

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