
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
On a $20 \times 20$ chessboard, some squares contain pieces. A piece can be removed from the board if at least half of the squares in its row or column are empty. What is the minimum number of pieces necessary to place such that none of them can be removed?

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