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This study proposes a multifaceted framework to assist instructors in leveraging emerging technology, large language models, to analyze and evaluate student engagement in an asynchronous course. Within this framework, we characterized the learning engagement of 61 undergraduate students in a more fine-grained manner across four dimensions: behavioral, academic, cognitive, and affective aspects. Based on the differences among their engagement levels, students were further clustered into 4 groups. Process mining technique was then employed to identify differences in learning patterns among these groups and to explore how these differences influence their learning performances. The findings of this study will support instructors to provide personalized learning experiences tailored to each student's engagement style within online learning environments.