I recommend Dior lipsticks.

This is Dior Rouge Ultra Care Liquid 998.

The color is really intense, so it's best to apply just a little bit to your finger and dab it on! The pigmentation is excellent, and it is a deep red. It has a slight pinkish tint, but since the color itself is so intense, it doesn't really show. If you apply it with a tip, the color payoff is so intense that you can achieve an over-lip look with just a tiny amount, haha. Still, I've been using it for over a year and it doesn't seem to be running out at all ㅠㅠ haha. Personally, the color is a bit too strong, but still, if you dab it on, the shade looks really pretty. I think it would be a perfect match for cool tones! This is a lipstick I bought with my own money, and I plan to keep using it.