
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
In how many ways we can paint a  $N \times N$  chessboard using 4 colours such that squares with a common side are painted with distinct colors and every  $2 \times 2$  square (formed with 4 squares in consecutive lines and columns) is painted with the four colors?

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