
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 chessboard  $1000 \times 1000$  is covered by dominoes  $1 \times 10$  that can be rotated. We don't know which is the cover, but we are looking for it. For this reason, we choose a few  $N$  cells of the chessboard, for which we know the position of the dominoes that cover them. 
Which is the minimum  $N$  such that after the choice of  $N$  and knowing the dominoed that cover them, we can be sure and for the rest of the cover?

(Bulgaria)

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