
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
Two equilateral triangles are inside a square whose side length is \(4\sqrt{3}\). Their bases are on opposite sides of the square, creating a rhombus where the triangles intersect. What is the area of this rhombus?
A) \(12\sqrt{3} - 12\)
B) \(16\sqrt{3} - 16\)
C) \(20\sqrt{3} - 20\)
D) \(24\sqrt{3} - 24\)

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