Nature of pure mathematics research
I'm a pure mathematician, and my first impression is that your question seems to be assuming a dichotomy in pure mathematics that isn't really there. The vast majority of pure mathematicians, it seems to me, at times have to deal with abstract structures and do the sort of "thinking and reasoning" with them that you've seen in your analysis and group theory courses. On the other hand, in a comment to another answer you defined tricks as "coming up with clever ways to prove certain things/attain certain results." My assertion is that according to this definition, virtually all research in pure mathematics involves the application of tricks. After all, there's only so much you can do that is of interest to the mathematical community that can be obtained purely by combining known results and definitions in straightforward ways.

Nevertheless, I should point out that pure mathematics does indeed lie on a spectrum when it comes to abstract reasoning versus clever problem solving. The former approach to mathematics is perhaps best epitomized by Alexander Grothendieck, who "avoided clever tricks that proved the theorem but did not develop insight. He likened his approach to softening a walnut in water so that, as he wrote, it can be peeled open 'like a perfectly ripened avocado.'" At the other extreme are mathematicians like Paul Erdos, who largely worked on concrete problems that one could solve using 'clever tricks'. (Although it should be pointed out that, as Federico Poloni noted in a comment, when one uses a trick more than once it becomes a method. Erdos' probabilistic method arose this way.) There is a nice quote about this approach to mathematics in Gowers' essay The Two Cultures of Mathematics:


  At the other end of the spectrum is, for example, graph theory, where
  the basic object, a graph, can be immediately comprehended. One will
  not get anywhere in graph theory by sitting in an armchair and trying
  to understand graphs better. Neither is it particularly necessary to
  read much of the literature before tackling a problem: it is of course
  helpful to be aware of some of the most important techniques, but the
  interesting problems tend to be open precisely because the established
  techniques cannot easily be applied.


Having said all of this, I'll reiterate what I said at the beginning of my answer. This is largely a false dichotomy, and the vast majority of mathematicians have to use both clever tricks and abstract reasoning in their research.