
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 will win if he can cover all marked cells with non-overlapping L-shaped triominoes (each L-shape covers exactly three cells and must stay within the borders of the grid). What is the minimum number of cells Petya must mark so that Vasya cannot win?

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