First, the term "triangulation" is no longer advised in mixed methods research because it has acquired too many meanings. So, just say something like "systematic comparisons."
Second, why do you feel that your need a "paradigm?" If you have a meaningful research question and an appropriate way to address that question, that is what really matters in any kind of research.
It is unfortunate that you are required to include such a statement, since the whole idea of paradigms as guiding research is rather old fashioned (it dates back to Lincoln and Guba's work in 1985). That said, the two most prominent paradigms in mixed methods research are pragmatism and critical realism.
Never the less, the whole topic of paradigms does continue to receive attention. I have thus attached a chapter that I wrote on this topic.