3 Steps To Think Like a Grandmaster by GM Igor Smirnov (in his "Remote Chess Academy" series) is a 20-minute video that offers what I consider as another useful and practical contribution to a chess improver's thinking process. It outlines three broad steps, which I'll paraphrase:
1) Identify reasonable candidate moves
2) Remove ones from consideration that do not advance your plan
3) Calculate the ones left for safety (in other words, blunder check), then select the most aggressive of the valid moves remaining
Any chessplayer who has looked at constructing or analyzing their own thinking process - my version is the Simplified Thought Process (that works) - knows that it can be easy to build a lot of complexity into it, a tendency which quickly becomes self-defeating. A well-defined thinking process should not attempt to incorporate the sum total of your chess knowledge; any attempts to do so remind me of the Jorge Luis Borges story "Del rigor en la ciencia" ("On Exactitude in Science") about the project to make a 1:1 scale map.
To simplify the process and make it effective, it is necessary to focus on the "meta-cognition" piece of it - which can be defined as thinking about how you think. On a practical level, this means coming up with a formula describing how best to focus your (limited) attention and energy on those discrete elements of playing chess which are most important in decision-making. Temposchlucker's blog is one amateur's outstanding example of devoting a lot of thought to thinking.
Returning to the video content, I would say that its focus on basic principles is its strength, including citing common (but still useful to hear) ones like seeking to improve your worst piece in the absence of other obvious candidate moves, and limiting your calculations to only those few moves and situations which require them. It will not answer all the necessary questions about your thinking process, and of course will only reflect your current chess strength in terms of evaluating candidate moves, tactical considerations, and strategic plans. However, sometimes sticking to first principles can indeed help cut through a lot of unhelpful noise, and help you focus on the signals the position in front of you is sending.
EDIT: Smirnov provides some similar follow-on thinking process illustrations in "How I went from 1600 to 2260 Chess Rating in 1 Year" - which isn't about chess training, as I originally thought, but is a useful adjunct to the concept of a simpler, principles-based thinking approach. Examples of muddled thinking around the 1600 level were especially relevant (and unfortunately familiar).