
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
Let  $n\geq 3$  a positive integer. In each cell of a  $n\times n$  chessboard one must write  $1$  or  $2$  in such a way the sum of all written numbers in each  $2\times 3$  and  $3\times 2$  sub-chessboard is even. How many different ways can the chessboard be completed?

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