
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
Given a table  $m\times n$ , in each cell of which a number  $+1$  or  $-1$  is written. It is known that initially exactly one  $-1$  is in the table, all the other numbers being  $+1$ . During a move, it is allowed to chose any cell containing  $-1$ , replace this  $-1$  by  $0$ , and simultaneously multiply all the numbers in the neighbouring cells by  $-1$  (we say that two cells are neighbouring if they have a common side). Find all  $(m,n)$  for which using such moves one can obtain the table containing zeros only, regardless of the cell in which the initial  $-1$  stands.

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