Large Language Models (LLMs) have recently developed new advanced functionalities. Their effectiveness relies on statistical learning and generalization capabilities. However, they face limitations in internalizing the data they process and struggle, for instance, to autonomously execute algorithms. In this paper, we investigate the possibility of extending these models'capabilities to algorithm execution through specialized supervised training focused on reasoning decomposition. We introduce a training model called LLM-DAL (Large Language Model - Decompositional Algorithmic Learning), through which we demonstrate that LLMs'ability to perform complex algorithmic inferences and generalize can be significantly improved when the training method is properly designed to guide the model in its learning process.