I liked this too, and given the sister comment asked for a more colloquial description, I came up with my own:
1) Instead of using firm statements attached to yourself like "I know" or "I think" use statements that are easier for you to contradict and discard without feeling like you are attacking or discarding yourself, like "it seems that..." or "it appears that...". Then you can say "it seems that X but in contrast it appears that Y". That is better than "I know X but I could be wrong because Y".
2) Don't immediately describe things as good or bad or the right way and the wrong way, that will prevent you from seeing an alternative solution because you will have automatically labelled it as wrong when you labelled something else as right. Instead of "that is bad" or "that is the right way" to "I feel this way because...". It is easier to change a decision based on knowing how you feel and have felt than when you have "money in the game" as having said (even to yourself) that something was the only right way.
[Note: In general, being able to step back and pick the right thing because it is right is useful, but only after you have honestly considered the situation in a fair and impartial way. Being too partial too quickly cuts off your ability to think and accept better solutions. If you already knew it, you could just choose, but the point is you are trying to think through it, which means you don't know but are evaluating how you feel and how things seem to be, but trying to uncover more.]
3) Understanding your current state of mind, and what state of mind would work better for the current task is important, so you can match those up, or at least understand more deeply. These are things like the appearance of things or imaginative situations (eikasia), good faith and trust or persuasiveness (pistis), discursive thought (dianoia), theoretical thought (techne), practical knowledge (phronesis), or intuition (noesis). [Note: my comments on the meanings of the Greek terms are probably wrong, but...] You could combine multiple of these to reach your goal; and you will often have a sequence of thoughts that are in different ones.
Introspection is _huge_. If you can understand and evaluate how you think and feel; you can start to move past that, or use it to your advantage, or see the flaw in your own reasoning, or be more observant, or form new habits, etc.
Personally, I like yoga for this reason; it helps to accept your feelings as they come and to observe them without immediate judgement. I think it helps in developing intuition, controlling your thoughts and emotions, etc.