
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
Quadrilateral $ABCD$ is a parallelogram. Its area is $50$ square units. Points $E$ and $F$ divide the side $AB$ and $CD$ in the ratio $2:3$ and $3:2$ respectively, from $A$ to $B$ and $C$ to $D$. If $G$ divides the side $BC$ into equal halves, what is the area of triangle $AEF$?

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