
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
The cells of a table **m x n**,  $m \geq 5$ ,  $n \geq 5$  are colored in 3 colors where: 

(i) Each cell has an equal number of adjacent (by side) cells from the other two colors; 

(ii) Each of the cells in the 4 corners of the table doesn’t have an adjacent cell in the same color. 

Find all possible values for  $m$  and  $n$ . 

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