Elaborating on a thought process.

In the pursuit of a universally usable thought process (TP), the following categories can be identified:

• Control beforehand.
• Looking for inspiration.
• Control afterwards.

I use the term "control" in stead of "checks" to avoid confusion with "giving check". I like to keep the TP as minimalistic as possible. It makes no sense to cover every exotic idea you can think of. The goal of a TP must be simplifying a complex position. The idea is, that as much as possible, the TP must be automated. That implicates that steps that can be envisioned as a picture are preferred. I formulate the steps as questions, you need to interrogate the position for answers.

Control beforehand.

• Is my king in check? 

 In an OTB game, this step can be skipped. Since if you don't know that your king is in check, you might be better off when seeking a hobby that suits you more. Although in time trouble, you see sometimes that kings are checked without both players noticing it.
When solving puzzles, it is a good idea to check if your king is in check, because if it is and you don't know it, you are wasting a lot of time. While controlling if your king is in check might take less than a second. It is a typical board vision exercise.

Looking for inspiration.
When doing tactical exercises, there are two questions to be asked (= my personal TP):

•  Which are the squares from which to attack?
• Which pieces are overworked?

When you are solving mate in ones, you don't have to look far for inspiration, since, well, you already know what the position is about. You better ask these questions:

• Is the box around the king closed?

If the answer is no, the following question should be asked:

• Which move fixes the hole in the box around the king while giving check at the same time?

If the answer is yes:

• Which move gives check?

In general, the category "looking for inspiration" should provide a list of candidate moves. For other problems than mate in one, I probably should dive deeper in the matter. But for mate in one, these two questions suffice. Checking the box around the king when doing mate in one "hard" is perfectly suited to train aura vision, a subject that happens to be a major weakness of me.

Control afterwards.
This category adds standard chess knowledge to a move. It takes in consideration all possible logical answers to your move.

• Is the piece you intend to move pinned against your king?
• Is the square that you intend to move to protected?
• Can the opponent interpose the intended check?
• Creates the intended move a new hole in the box around the king?

If you can answer all the blue questions from the three categories within, say, 5 seconds, there can't be going on much thinking in your head. That would be good enough for me. Since that equals about 12 mates per minute, that would be an outstanding performance. For mate in one "hard".