
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 identical chessboards (each with 8x8 squares) are overlapped, and one of them is rotated 45 degrees around its center. If the area of each square is 1, find the total area of the overlapping black squares.

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