
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 hexagon $ABCDEF$ is constructed such that each side is of length $3$. Points $G$, $H$, and $I$ are the midpoints of sides $AB$, $CD$, and $EF$, respectively. If the hexagon consists of equilateral triangles and additional line segments connecting these midpoints, what is the total area of the hexagon $ABCDEF$ plus the triangle $GHI$?
A) $\frac{225\sqrt{3}}{16}$
B) $\frac{216\sqrt{3}}{16}$
C) $\frac{234\sqrt{3}}{16}$
D) $\frac{243\sqrt{3}}{16}$

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