[Purpose/significance] Generative AI search engines are becoming the most frequently used and most dis⁃cussed search platforms. However, there remains limited understanding regarding the effectiveness of their system de⁃sign, their ability to support diverse task types, and their capacity to enhance search outcomes for individuals with dif⁃ferent learning styles. This study addresses these gaps to supplement research on search behavior and effectiveness within generative AI search environments in the field of interactive information retrieval. [Method/process] Based on a hierarchical interaction model, we used the New Bing website as our experimental system to investigate the relation⁃ship between system interactions (information resources, page presentation, and technical characteristics) and search effectiveness. We also examined how different task types (factual and exploratory) and learning styles (divergent, con⁃vergent, assimilative, and accommodative) influence user search behavior and search outcomes. [Result/conclusion] Most system interaction metrics correlate positively with search effectiveness at the user level, while cost- benefit search effectiveness relates solely to page layout and typography. Participants demonstrated richer search behaviors and superior search outcomes during factual tasks. Furthermore, significant differences in search behaviors emerged across the four learning styles, primarily reflected in query restructuring frequency and types. Search effectiveness vari⁃ations were equally pronounced, with participants exhibiting divergent learning styles reporting superior experiences in both quality satisfaction and perceived value.