Why do some people say "I was thinking and some, on the other hand, say I have been thinking. Since an English is not my native laungage, I am still little confused as to which of those two is correct and when each one of them is used.

Any help in clarifying this confusion is greatly appreciated.
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This helped!
Good answer, thanks for your explanation!
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Today my english teacher told me because "think" is a state verb the correct grammar is "I have thought", so "I have been thinking" is incorrect, are you agree?

This one is perfect.