
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 $5 \times 5$ grid, Petya marks several cells. Vasya wins if he can cover all these cells with non-overlapping and boundary-fitting L-shaped trominoes (each tromino covers exactly three cells and can be placed only along the cell outlines). What is the minimum number of cells that Petya must mark to prevent Vasya from winning?

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