
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
A square has a side length of \(4\). Two equilateral triangles are placed within this square such that their bases are on opposite sides of the square and they overlap. What is the area of the resulting rhombus formed by their intersection?
A) \(16\sqrt{3} - 16\)
B) \(12\sqrt{3} - 12\)
C) \(8\sqrt{3} - 8\)
D) \(4\sqrt{3} - 4\)

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