Some clarification on kelvins

Ok I have been getting really mixed messages and would love the final answer:

Veg: 6500k yes or no
Flower 2700k yes or no

And which is "warm" and which is "cool.

It seems everywhere I look, I get a different answer.

Thanks!

2000 - 3000k = warm white = most red in the spectrum = best for flower production.
3000 - 5000k = cool white = less red in the spectrum = ok for veg, ok for flower, not best for either.
5000 - 6500k = Daylight = most blue in the spectrum = best for vegetative growth.