
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 five types of "tetromino" shapes as shown on the left diagram, with a sufficient quantity of each type. In a $5 \times 5$ grid as shown on the right diagram, these tetrominoes need to be placed such that they may be rotated or flipped, each small square of the tetromino must overlap with a small square of the grid, and no two tetrominoes can have overlapping parts. What is the minimum number of tetrominoes that need to be placed such that no additional tetromino can be placed?

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