
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
Petya has 7 nails and a board of size $4 \times 6$ divided into 24 equal squares. To secure the board, nails need to be driven into the centers of some cells such that for each cell without a nail, there is at least one adjacent cell (sharing a side) with a nail. Suggest a way for Petya to do this.

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