
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 $ABCD$, $AB = 6$ and $BC = 4$. Points $F$ and $G$ are on $\overline{CD}$ such that $DF = 2$ and $GC = 1$. Lines $AF$ and $BG$ intersect at $E$. Find the area of $\triangle AEB$.

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