The question might be, when on your turn can you normally take actions?
All the book says is you can choose to move or take an action first on your turn. Bonus actions don't actually exist unless you have the ability to take them- that is, you don't have a bonus action by default. Something has to give you one. And unless timing is specified, these can be done at any time. Similarly, reactions happen as an instant response to their trigger.
So from this, you might say that a turn looks like this:
1- Move or take an Action.
1b- if you Move, you need not use all of your Speed before you take an Action. You can choose to use unused Speed after an Action.
1b- you can stand up from Prone or fall Prone whenever you can move. Going Prone costs 0 Speed, standing up again costs half your remaining Speed.
1c- if you take the Attack Action and make a weapon attack, you can split your movement between the individual weapon attacks.
2- if you have taken an Action and used up all of your Speed, your turn is done.
2a- bonus actions. If you have an ability that uses a bonus action, you can take this bonus action at any time during your turn you are allowed to do so.
2b- you can use a reaction to instantly respond to a triggering event at any time during your turn (or on someone else's turn), such as making an Opportunity Attack (the most common reaction).
2c- things a character can do which are not actions can be done at any point in their turn. This is a slight extrapolation from the text on page 190 of the PHB, "Other Activity On Your Turn". I believe that things like going Prone/Standing up from Prone and the "free" interact with an object (which is otherwise functionally identical to the Use and Object Action) slot into here, as does anything else that doesn't require an action to accomplish, such as Smite or deciding to use Action Surge.
Additional Actions granted by effects such as Haste or Action Surge have no stated qualifiers as to when they can be taken, beyond when you can take an Action. The only limitation on Action Surge is that it can be only used once per turn (at 17th level, when you gain a second use of this ability). The only limitation on Haste is what kind of Action can be used- Attack (one weapon attack only*), Dash, Disengage, Hide, or Use an Object action.
*This is interesting and something I never noticed before- a character cannot make an Unarmed Strike/attack with a natural weapon using Haste. I had to check the Clay Golem, and sure enough, it's version of Haste allows a Slam attack as a bonus Action, instead of affording it an additional Action.
Ok, so now that that's been established, can a discrete Action occur during another Action? I've finally landed on "maybe". This isn't really a copout, inasmuch as the rules themselves aren't written in a legalistic fashion. In the spirit of "rulings not rules", the DM decides, just as they decide if something a player wishes to do requires an action in the first place (at several points in the text, such as "Actions in Combat" on page 192 of the PHB, the text will state things such as "the DM tells you whether that action is possible and one kind of roll you need to make" or "Use an Object" on page 193 "When an object requires your action for it's use".
So the DM decides if and when an action can be performed. If it seems logical to them, there's no reason you couldn't, say, Action Surge Dash between attacks. If not, say like casting a leveled spell, you can't.
If I had an enemy suddenly turn invisible in the middle of a Fighter's attack routine, if they had the ability to reveal that foe, either by Use an Object to toss a bag of flour, or casting Faerie Fire, I don't see any reason to prevent this, and I would argue that this is, in fact, the Fighter's whole thing, being a master of tactics, so naturally I feel they should be able to respond to the changing battlefield in ways other characters cannot.
That having been said, a blanket ruling on this topic might open up something abusive. I don't know what that is, but I'm sure others will have something that they feel is "out of bounds" for whatever reason, thus leaving this up to the DM's ruling is probably the correct call.
Similarly, using Ready an Action to set up a trigger that occurs after your first attack, while legal, is also subject to the DM's ruling if a trigger is viable. Though I would expect (rightly) some outcry if I said "you can't set -after I attack with my sword- as a trigger", lol.
It's not that 5e's design team couldn't think of every corner case- they felt that, at the end of the day, common sense should prevail. While I certainly would prefer more text to avoid more of these corner cases, my experience has been that if a DM disagrees with a rule, they'll likely ignore it anyways, so why waste the ink? My DM thinks forcing Clerics to drop or put away their melee weapons to cast a spell while using a shield is dumb, for example. So he doesn't enforce that rule, despite it being spelled out in the PHB.
Even when they did have more in-depth rules (ala 3e), it didn't alter the prevalence of rules debates one iota!
If, after reading this, you find yourself asking "why do we even need rules anyways, beyond, The DM Decides?"...I have no idea what to say. I know I would reject such a system on it's face, unless I had great trust in my DM (which is why I stopped playing Amber). But I know that a detailed rules system doesn't prevent bad experiences. Each group has to negotiate a happy medium between DM authority and accepted practices to function. No rules system, no matter how well-crafted, can replace this necessity.
