Assuming that no two areas on the same side have the same color at this time, adding a line (passing through several areas but not passing through the intersection) will still meet the above conditions, but the areas on the same side of the added line are the same color (divided by the same area), so as long as all areas on both sides of the line change colors, the conditions can be met.

That is, without adding a line, the color on one side of the line remains unchanged, and the color on the other side changes.