
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
Find all positive integers  $ n $  with the following property: It is possible to fill a  $ n \times n $  chessboard with one of arrows  $ \uparrow, \downarrow, \leftarrow, \rightarrow $  such that 

1. Start from any grid, if we follows the arrows, then we will eventually go back to the start point.

2. For every row, except the first and the last, the number of  $ \uparrow $  and the number of  $ \downarrow $  are the same. 

3. For every column, except the first and the last, the number of  $ \leftarrow $  and the number of  $ \rightarrow $  are the same.

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