
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
How many cells need to be marked on an 8 by 8 chessboard so that each cell on the board, including the marked ones, is adjacent by a side to some marked cell? Find all possible answers. Assume that a cell is not adjacent to itself.

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