
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
A rectangle ABCD has an area of 108 square meters. Point E is the midpoint of side AD, and point G is one-third of the way along side CD from C towards D. Point F is the midpoint of side BC. Calculate the area in square meters of trapezoid DEFG.
A) $\frac{36}{a} + 9$
B) $18 + \frac{18}{a}$
C) $24 + \frac{24}{a}$
D) $15 + \frac{10}{a}$
E) $30 + \frac{12}{a}$

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