
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 trapezium $ABCD$, $AB=2$, $CD=4$, and $BC=3$, with $AB$ and $CD$ parallel, the points $E$, $F$, and $G$ are midpoints of $\overline{BC}$, $\overline{CD}$, and $\overline{AD}$, respectively.  Point $H$ is the midpoint of $\overline{GE}$. Calculate the area of the quadrilateral formed by the points $E$, $F$, $G$, $H$.
A) 0.5
B) 0.75
C) 1.0
D) 1.25

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