
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
Let $ABCDEF$ be a regular hexagon, and let $G, H, I$ be the points such that $G$ is the midpoint of side $AB$, $H$ is the midpoint of side $CD$, and $I$ is the one-third point from $E$ to $F$ on side $EF$. If the area of $\triangle GHI$ is $100$, what is the area of hexagon $ABCDEF$?

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