
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 $8 \times 8$ cells) share a common center, with one of them rotated by $45^{\circ}$ relative to the other around the center. Find the total area of all intersections of the black cells of these two boards if the area of one cell is 1.

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