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Training your thought process

IM Silman in his book: How to Reassess Your Chess suggests the following method for every move: First evaluate the position and work out the imbalances, then form a plan, then select candidate moves, find out the possible responses to those moves and lastly start to calculate.
Jacob Aagaard writes in one of his books about positional play that there are only 3 questions which you have to answer in any position.

1. What are the weaknesses (for White and Black) ?
2. What is the worst positioned piece (for White and Black) ?
3. What will be the next move of your opponent ?

If you can answer these questions then you know your next move.
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There was one pioneer who was "building" an algorythm in his head... he wanted to do that in 30 days... he challenged World CHampion to prove everybody wrong... he tried to surprise Magnus with his unorthodox and out of any patterns thought process... maybe he didn't win that game, but Magnus couldn't win smoothly either
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@TrainingOTB

It doesn't get smoother than that. I could crush that pioneer and so could you.
A noob can use whatever algorithm, without patterns/intuition they are out of their depth.
Reassess Your Chess is a great asset in terms of highlighting fundamental instances that are always noteworthy and relevant to different positions; however, it is also extremely counter-productive in terms of attempting to produce a 'step-by-step' academic exercise out of the process of creating a good chess move.

To answer your question in one way:

If you try to write on paper the thought process that's needed to process any board position, you will end up with an encyclopedia that has 20 chapters, with each chapter having a-z modules, and with each module having i-x sub-sections.

"When ___ is present in the position, then ___, unless ___. If ___ is the case, but not ____ then ___ should be considered, unless ___ where then ___ would be the way to play, unless ___ is in the position. If ___ is the case, then ____ and then ____ would be the move."

There is no way to structure any kind of a rigid or dogmatic structure.

Different positions require different ideas. It all depends on where all of the pieces are placed, and exactly what they are doing there.

To answer your question another way:

With that said, you'll want to start with a cursory 'tactical puzzle' perspective where you're looking for anything that is 'blink and miss'. This often means needing to push/capture a pawn, where if you don't, your opponent will gain a permanent fundamental advantage by pushing/capturing on the next turn; this could mean moving a bishop to a more active square, where, if you failed to do so immediately, you would be stuck with a bad bishop for the rest of the game; this could mean doing a quick 'blunder check' to make sure that none of yours (or your opponent's) pieces can be easily captured or trapped or checkmated in the next few moves.

If there is nothing immediate, if there is nothing pressing, if there is nothing that you need to do right here and right now; if there are no 'final off-ramp' or 'blink-and-miss' or 'now-or-never' instances to pay attention to, then go ahead and switch channels into 'creative mode' where you will find a fundamental gain to implement, and/ a fundamental deficit that you can impose on your opponent.

Once you find an argument to play for, once again, switch back to 'tactical-mode' where you then crosscheck your idea for subsequent tactics. (If you diagnose that you need to play for control of a file, and you have a plan to take control, that's all fine and well, but if that plan will leave something split or trapped or give up an even bigger fundamental/tactical deficit somehow, then that should be understood and avoided.)

It's a matter of what you have to do vs. what you want to do vs. what's logistically/tactically justified/allowed/available.

1-2-3.
Interesting thoughts so far, thanks!

I should probably clarify - when I talk about structuring your thought process or whatever, I'm not imagining that good chess players are necessarily sat there consciously working through checklists and flowcharts in their heads or thinking "right, are there any checks and captures that I should consider?" More that consciously thinking about that sort of stuff often seems to be a useful step in developing a better instinctive awareness of what you ought to be doing...
Step one: forget all your lists
Step two: forget everything else as well
Step three: burn your old books
Step for: get yourself MFTL and read it with a fresh mind

movefirstthinklater.com/
Burning books makes me sad.
I like MFTL because it's fast way of arriving at a solution.
But sometimes I get stuck and that's when it's nice to be able to shift gear and go down the analytical path.
Find a good method. Understand the method and the reasons for each methodical step in the method. Then repeat in your (longer time control games). Constantly and repetitively build up your chosen method of structured thought process until it becomes part of muscle memory, er, in this case brain memory. Eventually, it should become automatic and reflexive.

P.S. I'm not there yet. But I talk a good game, lol.
There's no hard and fast algorithm. People can't process information like computers nor should they try to. Just work on honing your instincts one position at a time. And what that really comes down to is analysis.
@tpr I liked your answer. My problem is with the blunder check. As most of my blunders aren't blunders because something is hanging or unsafe, but because of a lost opportunity like missing a tactic or not finding the move to punish a blunder of my opponent. How can I check for this sort of blunder`? It is easy to check if your king and pieces are safe, but how to blunder check in a sense of "did I not see something"? You cannot ask yourself every move if you missed something, that way you'll actually might go insane xD There is the "Is there a better move"-thought-approach but it isn't exactly what I mean. Sometimes you just don't realise a blunder of your opponent and think it is good.

Example: I missed Qf4+ winning the knight:

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