This study investigates the approach of integrating reasoning into the outputs of large language models (LLMs) — combining logical inference techniques with knowledge retrieval — to enhance their alignment with truth. We begin by analyzing the statistical foundations of LLMs, which operate as probabilistic text generators based on Markovian assumptions without genuine semantic understanding. Next, we discuss the conceptual framework of 'truth' in the AI context, differentiating between descriptive truth (objective correctness), pragmatic truth (contextual utility), and verifiable knowledge (information supported by independent evidence). We examine advanced reasoning techniques — from Chain-of-Thought [1], Tree-of-Thought [2], Retrieval -Augmented Generation [3], to self-critique models like CriticGPT [4] - that move LLMs closer to verified knowledge and mitigate hallucination tendencies. The paper also explores the philosophical implications: Can modern LLMs, equipped with reasoning capacities, be considered 'fallible cognitive agents' - akin to humans in their capacity for error correction and learning -or are they merely stochastic parrots mimicking language without true understanding? Finally, we open a discussion on the risks, limitations, and ethical issues involved in deploying reasoning-integrated AI systems, connecting them with contemporary philosophical currents such as pragmatism, anti-realism, and behaviorist perspectives in evaluating artificial intelligence.