
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 rectangle $ABCD$, where $AB = 2$ and $BC = 3$, points $E$, $F$, and $G$ are placed as follows:
- $E$ is the midpoint of $\overline{BC}$,
- $F$ is at the quarter-point on $\overline{CD}$ (i.e., nearer to $C$),
- $G$ is at the three-quarter point on $\overline{AD}$ (i.e., nearer to $D$).
Point $H$ is the midpoint of the segment connecting $G$ and $E$. What is the area of the quadrilateral formed by connecting points $A$, $F$, $H$, and $D$ sequentially?
- **A)** $\frac{1}{4}$
- **B)** $\frac{1}{2}$
- **C)** $\frac{3}{4}$
- **D)** $1$
- **E)** $\frac{5}{4}$

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