
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
Some  $1\times 2$  dominoes, each covering two adjacent unit squares, are placed on a board of size  $n\times n$  such that no two of them touch (not even at a corner). Given that the total area covered by the dominoes is  $2008$ , find the least possible value of  $n$ .

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