
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
There is a \(2018 \times 4\) grid where each cell is colored either red or blue, such that in every row, the number of red and blue cells is the same, and in every column, the number of red and blue cells is the same. Let \(\mathrm{M}\) be the number of coloring methods that satisfy these conditions. Find the remainder of \(\mathrm{M}\) when divided by 2018.

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