In the first sense actually, like really, is a useful word, especially in speech. It is used to reinforce or emphasize a point and can enhance the continuity and balance of a sentence: ‘I told you.’ ‘Actually, I don't think you did.’ (Here, actually softens the contradiction.) But with frequent use it can become irritating, especially in writing and when it is clearly redundant, i.e. when the sentence would mean exactly the same without it and it hardly improves the flow: It's actually quite cold. Did you actually mean that? Actually, I think I'll stay here