As a Persian speaker, we do use "In fact" and "Actually" in the spoken and written language. And it is quite formal. I think when we want to add more details to something, or say something in another way (as it is in other words, however we have this phrase too), or to be more clear and factual and direct we use it.
But as I used it in some English sentences, I am told that is informal! OK, then what are the formal ways for it?.
For example these are some literal translation of the phrase usage in my language and I do feel a need for a formal equivalent phrase (for "in fact", and "actually") in English.
In this paper we do this..., In fact we simulate the way a human user do this.
We should help each other, in fact it is the sign of our humanity.
A pregnant woman shouldn't smoke, in fact, smoking pose hazards for the infant.