
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
On the sides of an equilateral triangle, squares are constructed outside of it. The vertices of these squares, which lie outside the triangle, are connected in sequence. Determine the area of the resulting hexagon if the side of the given triangle is \(a\).

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