Approaches to supporting creativity are diverse and numerous. Making sense of these methods, including the comparative benefits of one approach over another is highly significant to both research and practice of creative design. This paper demonstrates the benefit of conducting analyses of methods with the aid of a theory. Such an approach provides a clear basis for analysing different methods that could in turn be compared with each other. This approach is demonstrated through the critical analysis of advanced systematic inventive thinking (ASIT) - a practical method - using the C-K theory, a design theory that offers a formal model of creative thinking. The analysis uncovers a paradox in ASIT operation: being creative while 'staying in the box'. While confirming that ASIT could be perceived as an implementation of some of the C-K constructs, the analysis further resolves the paradox by explaining how creative solutions could be created with ASIT. Finally, the analysis also exposes the capabilities and limitations of ASIT as well as its directions of improvement by extending ASIT operators and applying them in a linear manner.