As the recent Large Language Models(LLM's) become increasingly competent in zero-shot and few-shot reasoning across various domains, educators are showing a growing interest in leveraging these LLM's in conversation-based tutoring systems. However, building a conversation-based personalized tutoring system poses considerable challenges in accurately assessing the student and strategically incorporating the assessment into teaching within the conversation. In this paper, we discuss design considerations for a personalized tutoring system that involves the following two key components: (1) a student modeling with diagnostic components, and (2) a conversation-based tutor utilizing LLM with prompt engineering that incorporates student assessment outcomes and various instructional strategies. Based on these design considerations, we created a proof-of-concept tutoring system focused on personalization and tested it with 20 participants. The results substantiate that our system's framework facilitates personalization, with particular emphasis on the elements constituting student modeling. A web demo of our system is available at http://rlearning-its.com.