When I say cool, I don't necessarily mean in fighting. The coolness could be from different categories. Basically I don't want a bumbling idiot who's always clumsy and falling down. It could be that she wears cool clothes (suit, jackets, etc) or is well educated with a good job or can think rationally. It could be any genre but I want it together with romance
The woman on my mind when writing this is An Di from Ode to joy she was so cool to me

P.S I would like to avoid K-dramas as much as possible