
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
Each side of a unit square (side length 1) is also one side of an equilateral triangle that lies in the square.  Compute the area of the intersection of (the interiors of) all four triangles.

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