
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  $ m\geq n\geq 4$  be two integers. We call a  $ m\times n$  board filled with 0's or 1's *good* if

1) not all the numbers on the board are 0 or 1;

2) the sum of all the numbers in  $ 3\times 3$  sub-boards is the same;

3) the sum of all the numbers in  $ 4\times 4$  sub-boards is the same.

Find all  $ m,n$  such that there exists a good  $ m\times n$  board.

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