
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 the set
$$
M=\{1,2, \cdots, 2020\} \text{.}
$$

Each number in $M$ is colored with one of three colors: red, yellow, or blue, ensuring that each color is used at least once. Define
$$
\begin{aligned}
S_{1}= & \left\{(x, y, z) \in M^{3} \mid x, y, z \text{ are the same color and } 2020 \mid(x+y+z)\right\}, \\
S_{2}= & \left\{(x, y, z) \in М^{3} \mid x, y, z \text{ are all different colors and } 2020 \mid(x+y+z)\right\}.
\end{aligned}
$$

Find the minimum value of $2\left|S_{1}\right|-\left|S_{2}\right|$.

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