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This is more of a culture question than a language question, but the two can't always be separated, can they?
For me, one of the most shocking things about the United States was how often people ask "How are you doing?" The first thing the cashier in a shop says to customers is this. So obviously, this is a form of greeting, and not a genuine interest in one's wellbeing.
It reminds me of "How do you do?" from my very old fashioned (British) English textbooks, which taught us that the correct response to this is simply "How do you do?"
So, what is the correct and polite response to "How are you doing?" in the United States?
Can I just say, "How are you doing?", or do I need to reply with "Good." first?
Or just say "Good", and leave it at that without asking the other person the same question?
Can I just simply say "Hello"?
It still feels like a genuine question to me, so it's hard not to reply. But it also feels very awkward to say it so many times each day.