
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
Every cell of a  $m \times n$  chess board,  $m\ge 2,n\ge 2$ , is colored with one of four possible colors, e.g white, green, red, blue. We call such coloring good if the four cells of any  $2\times 2$  square of the chessboard are colored with pairwise different colors. Determine the number of all good colorings of the chess board.

*Proposed by N. Beluhov*

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