Intermittently, as the understanding of the unfolding situation demands. "I see an object moving down, thus it is likely falling", which is in contrast to LII's "The object is falling, thus it should be moving down". In other words, while LII can take a logical structure and derive possible conclusions about situations it represents, ILE progresses in the opposite direction by taking their intuition of the current situation and deriving possible logical structures that would explain it.
Very quickly and, admittedly, sloppily, because the primary goal of using Ti tends to be making a fast decision as the situation unfolds, i.e. it is first and foremost driven by their Ne. "I understand everything very easily but not necessarily correctly" could be the motto of being an ILE.
You don't look for them specifically, they come to you through your life experiences. Usually, you just McGuiver it with whatever is available to you. ILEs are always on the lookout for new ideas that they later use to expand their arsenal of quick solutions.
This is a very difficult question, because to me this process seems largely transparent when at work, but I would assume most definitions are through examples and associations, i.e. "Given A, B and C, X tends to act like Y and Z". When something new is introduced into the equation, the first thing I personally would do is to experiment with it to see how it would react, so that I can build a quick understanding through already familiar objects that react similarly.
Edited to add:
In hindsight it seems evident that my explanation here is strongly tainted by my strong Se. In reality, an average ILE would probably focus more not on the current situation unfolding (as that requires strong awareness of the here and now), but on different possibilities and imagined futures. In other words, a more balanced ILE would imagine something and derive possible explanations and maybe even solutions how to achieve it reasonably.




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