Argument mining (AM) focuses on analyzing argumentative structures such as Argument Components (ACs) and Argumentative Relations (ARs). Modeling dependencies between ACs and ARs is challenging due to the complex interactions between ACs. Existing approaches often overlook crucial conceptual links, such as key phrases that connect two related ACs, and tend to rely on cartesian product methods to model these dependencies, which can result in class imbalances. To extract key phrases from the AM benchmarks, we employ a prompt-based strategy utilizing an open-source Large Language Model (LLM). Building on this, we propose a unified text-to-text generation framework that leverages Augmented Natural Language (ANL) formatting and integrates the extracted key phrases inside the ANL itself to efficiently solve multiple AM tasks in a joint formulation. Our method sets new State-of-the-Art (SoTA) on three structurally distinct standard AM benchmarks, surpassing baselines by up to 9.5% F1 score, demonstrating its strong potential.