
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
A piece is placed on a cell of a $7 \times 7$ board. It is allowed to sequentially place new pieces on empty cells, but in such a way that each cell on which a new piece is placed shares a side with no more than one already occupied cell. What is the maximum number of pieces that can be on the board after several such operations?

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