
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

Some gray pieces in the shape of a $2 \times 1$ domino can be used to cover the squares of a $5 \times 5$ board. We say that the board is crowded when there is no space to place new pieces, as in the example below. What is the minimum number of pieces required to leave a board crowded?

![Example](https://cdn.mathpix.com/cropped/2024_05_01_3fc4f3a6ef7302a792fcg-28.jpg?height=367&width=365&top_left_y=615&top_left_x=732)

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