
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 the diagram, triangle $ABC$ and square $DEFG$ are on a plane. Triangle $ABC$ is an equilateral triangle with each side measuring 6. Square $DEFG$ has side $DE = 6$ and is positioned such that point $D$ is exactly at the midpoint of segment $BC$. Find the total area of the shape formed by $ABCGDE$.

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