Short Text Classification (STC) is crucial for processing and comprehending the brief but substantial content prevalent on contemporary digital platforms. The STC encounters difficulties in grasping semantic and syntactic intricacies, an issue that is apparent in traditional pre-trained language models. Although Graph Convolutional Networks enhance performance by integrating external knowledge bases, these methods are limited by the quality and extent of the knowledge applied. Recently, the emergence of Large Language Models (LLMs) and Chain-of-Thought (CoT) has significantly improved the performance of complex reasoning tasks. However, some studies have highlighted the limitations of their application in fundamental NLP tasks. Consequently, this study sought to employ CoT to investigate the capabilities of LLMs in STC tasks. This study introduces Quartet Logic: A Four-Step Reasoning (QLFR) framework. This framework primarily incorporates Syntactic and Semantic Enrichment CoT, effectively decomposing the STC task into four distinct steps: (i) essential concept identification, (ii) common-sense knowledge retrieval, (iii) text rewriting, and (iv) classification. This elicits the inherent knowledge and abilities of LLMs to address the challenges in STC. Surprisingly, we found that QLFR can also improve the performance of smaller models. Therefore, we developed a CoT-Driven Multi-task learning (QLFR-CML) method to facilitate the knowledge transfer from LLMs to smaller models. Extensive experimentation across six short-text benchmarks validated the efficacy of the proposed methods. Notably, QLFR achieved state-of-the-art performance on all datasets, with significant improvements, particularly on the Ohsumed and TagMyNews datasets.