Evoking a new way of thinking.
The quality of being discerning, sound in judgment, and
farsighted; wisdom. Prepared.
If "simple perceptions" are potentially inadequate to serve as the basis for a sound judgment, then one needs to know both when more is needed and what that more might be. Such knowledge (or the ability to discern it) is the kind of preparedness which our "normal" understandings of common sense lack. If we can add such knowledge to our basic common sense understandings, we will be much better prepared to face the "non-simple" portions of the world.
One framework for doing so is the Cynefin perspective developed by David Snowden. Cynefin is a Welsh word meaning a combination of "habitat" or "place" combined with both "history" and the "habitus" of Bourdieu (i.e. the lifestyle, the values, the dispositions and expectation of particular social groups which are acquired through the activities and experiences of everyday life). The Cynefin framework is a tool used to survey the present context (i.e. the "place") in order to better determine how to approach it.
Using the Cynefin framework, one discovers that the common sense approach of "sense, categorize, respond" is appropriate only in the "simple" domain. As situations/context grow more complicated and then complex, the notion of how to approach them changes. It is this notion of applying different approaches to different domains that gives the Cynefin framework its power and which allows its user to add some sagacity to simple common sense.
See: David Snowden explaining the Cynefin Framework.