The phrase "actually assume" is correct and usable in written English.
It can be used when you want to emphasize a belief or conclusion that is being taken as true, often in contrast to a previous assumption or expectation.
Example: "While many people think the project will fail, I actually assume it will succeed based on the data we've collected."
Alternatives: "truly believe" or "genuinely think".
Cake Boss could actually assume some of the organised crime credentials he clearly wishes he had in real life.
My instinct is that it's better to keep the ratings agencies as heavily-regulated public utilities than have the government actually assume their function.
But other analysts doubted Stymiest, if named to the chairmanship, would actually assume the transformational role that activist shareholders are calling for.
When we left our characters last year, the question remained as to who would actually assume a leadership role within Empire.
Many species immediately abandon the eggs; some remain with the clutch and certainly appear to be protecting them from external danger; and a very few actually assume the role of a brood hen, maintaining a body temperature measurably higher than the surroundings and presumably assisting in incubation.
Undoubtedly stimulated by the once widespread superstition that lycanthropy is a supernatural condition in which men actually assume the physical form of werewolves or other animals, the delusion has been most likely to occur among people who believe in reincarnation and the transmigration of souls.
For a long time there was no fixed rule as to the necessary or allowable number of sponsors, and sometimes the number actually assumed was large.
Pharmaceutical R&D, education materials, expansion in Nairobi – these are just causes, but are the recipients worthy of the gifts, given how little financial risk they're actually assuming?
Moore actually assumed the Tories were going to lose the 1983 election, and that Labour would remove nuclear weapons from British soil – thus paving the way for the avoidance of nuclear catastrophe that engulfs the rest of his unhappy world.
In another chapter, at the conclusion of an otherwise deliciously squalid account of the self-righteous hippie tripfest known as Burning Man, LeDuff actually assumes the role of God, a choice both perplexing and redundant.
When administration lawyers expressed worry that Mr. Obama had not actually assumed the presidency, a do-over was quietly arranged the next day in the Map Room of the White House.
