
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
In the cells of an $8 \times 8$ board, the numbers 1 and -1 are placed (each cell contains exactly one number). Consider all possible positions of a shape $\square$ on the board (the shape can be rotated, but its cells must not go out of the board). We call such a position unlucky if the sum of the numbers in the four cells of the shape is not equal to 0. Find the smallest possible number of unlucky positions.

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