
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
Right triangle $\triangle ABC$ with legs $AB = 3$ and $AC = 4$ and hypotenuse $BC=5$ has rectangles $ABDE$, $BCFG$, and $CAHI$ constructed outside it such that each rectangle shares one side with the triangle. $ABDE$ and $CAHI$ are squares with areas $9$ each, while $BCFG$ is a rectangle where $BF=BC=5$ and $BG=6$. Find the area of hexagon $DEFGHI$.

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