The advent of Large Language Models (LLMs) has profoundly transformed the paradigms of information retrieval and problem-solving, enabling students to access information acquisition more efficiently to support learning. However, there is currently a lack of standardized evaluation frameworks that guide learners in effectively leveraging LLMs. This paper proposes an LLM-driven Bloom's Educational Taxonomy that aims to recognize and evaluate students' information literacy (IL) with LLMs, and to formalize and guide students practice-based activities of using LLMs to solve complex problems. The framework delineates the IL corresponding to the cognitive abilities required to use LLM into two distinct stages: Exploration & Action and Creation & Metacognition. It further subdivides these into seven phases: Perceiving, Searching, Reasoning, Interacting, Evaluating, Organizing, and Curating. Through the case presentation, the analysis demonstrates the framework's applicability and feasibility, supporting its role in fostering IL among students with varying levels of prior knowledge. This framework fills the existing gap in the analysis of LLM usage frameworks and provides theoretical support for guiding learners to improve IL.