How do I look like cool solitary girl instead of lonely one?

I used to think I'm being kinda pathetic for being on my own at public spaces. But i just wanna do things calmly, without looking like someone who's lonely. People pass by and like ask me if I'm okay, in the sense like I'm sad or something. But I wanna be the cool girl alone, enjoying of her own company - which is true. How can I demostrate that? I'd take your advices, please help :(
How do I look like cool solitary girl instead of lonely one?
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