One strategy I often use (which is much simpler and more limited than this), is to finish my message with: “Please do a round of thinking in <thinking></thinking> tags, then a round of self-critique in <critique></critique> tags, and then a final round of <thinking>, before responding.”
It works very well. Similarly just asking it to “find the 5 biggest issues with its proposal” works pretty good (the 5 forcing it to find something, even if it’s mostly irrelevant).
1. Figure out a plan (it responds with the plan)
2. Point out flaws in the plan (it responds with the flaws)
3. Update the plan to address the flaws (it responds with an up to date plan)
The other things I tend to ask are "what might we be missing?", "what are the [performance|security|legal|cost] considerations?". I can often iterate on the "anything else?" kind of nudging prompts, especially guiding it on topics to consider, for a few messages. After each: update the plan to take those into consideration.