
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
There are  $2020\times 2020$  squares, and at most one piece is placed in each square. Find the minimum possible number of pieces to be used when placing a piece in a way that satisfies the following conditions.
・For any square, there are at least two pieces that are on the diagonals containing that square.

Note : We say the square  $(a,b)$  is on the diagonals containing the square  $(c,d)$  when  $|a-c|=|b-d|$ .

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