AP controls Lantern of Insight and casts Ancient Stirrings, looking at the top 5 cards. If AP chooses to reveal the top card of the library and puts it in their hand, is the second card down (now the new top of the library) revealed before the four cards are put to the bottom of the library in any order? From this article:

https://blogs.magicjudges.org/rulestips/2014/10/courser-of-kruphix-and-dig-through-time/

if Ancient Stirrings was swapped with Dig Through Time, the answer is no. But there's a subtle wording difference between the two cards: Dig Through time states to choose two and put the rest on the bottom in one clause, while Ancient Stirring states reveal one card and put it in hand. Then put the rest on the bottom in any order. Does that clause separation and wording difference change what happens?

If one cracks a fetch (while Lantern is in play) and selects the top card as the land to come into play, I know they have to reveal the next card before shuffling. For a fetch, the wording also has a “Then shuffle your library” clause as a separate sentence. By that similarity, I could guess the answer may be yes, however I also recognize that one situation involves searching the library, while the other has to do with looking at the top of it. I don't know if that makes a difference, but I am curious to find out/and if so why?