
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
Trapezoid $ABCD$ (with $AB$ parallel to $CD$) has area $50$ square units. Points $E$ and $F$ are the midpoints of non-parallel sides $AD$ and $BC$, respectively. Diagonal $AC$ intersects $EF$ at point $G$. If trapezoid $ABEF$ has an area of $20$ square units, find the area of triangle $AEF$.

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