
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 trapezoid $ABCD$, sides $AB$ and $CD$ are parallel with lengths of 10 and 30 units respectively, and the altitude from $A$ to $CD$ is 18 units. The diagonals $AC$ and $BD$ intersect at point $G$, which divides $AC$ in the ratio 1:2 starting from $A$. Points $E$ and $F$ are the midpoints of $AD$ and $BC$ respectively. Calculate the area of quadrilateral $EFCD$ in square units.

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