The default pattern for initiative is a single character goes, which produces the feeling that everyone watches one another and then responds. This initiative system seeks to break up the semi-individualistic flow to combat and other initiative scenarios. A player's turn is broken into two parts, which still require each character in the initiative to respond to others, but how they respond is a two-step process than an all-in-one action.
Action Economy Flow
A Round is composed of two Sequences, the Move Sequence and the Action Sequence. A Sequence completes when every character involved in the Sequence completes its Turn. A Round completes when both Sequences have completed.
A Turn represents each character's decisions during a Sequence. The next Sequence begins when each character completes their Turn in the current Sequence. Turns are taken in the order of Initiative.
Some Actions can be performed outside of their current Sequence through use of the Free Action and the Reaction.
Each character performs their move action during this Sequence. A move action requires the use of a character's speed. A character may use as much of or as little of their speed as desired. Once each character has made their move, the Sequence ends. Characters who do not use their entire speed during the Move Sequence may use half of the remaining amount during the Action sequence.
Each character can perform an action during their Turn during the Action Sequence. The Action Sequence ends when all characters have taken their Action. Turns are determined by the Initiative Order.
The Ready Action
The ready action allows a player to defer their Action Sequence Turn until a later time given a specific trigger. A readied action can occur during the Move or Action Sequence because it requires the use of the Reaction.
Bonus Actions are used during their specific trigger or during the character's Turn in the Action Sequence.
Characters can perform free actions either when the trigger becomes available, or once per Round during either sequence to interact with an object.
A character's reaction can be used during the Move or Action Sequence whenever its trigger occurs, but only once per Round unless an ability states otherwise.
Order of Turns
The order of Turns is dictated by the initiative order. Initiative order is rolled at the start of a situation requiring a determination of initiative. A Dungeon Master may determine whether or not initiative needs to be rolled again at the start of a later Round, perhaps when a profound event occurs.
As an alternative to the above, initiative may be rerolled at the start of every Round, indicating possible changes within the flow of a situation.
This has the potential for wasted move actions but could create more uncertainty as to the results of a move or an action, since these things aren't seen until the second sequence.