Negotiation requires dynamically balancing self-interest and cooperation within the flow of conversation to maximize one's own utility. Yet, existing agents struggle due to bounded rationality in human data, low adaptability to counterpart behavior, and limited strategic reasoning. To address this, we introduce principle-driven negotiation agents, powered by ASTRA, a novel framework for turn-level offer optimization grounded in two core principles: opponent modeling and Tit-for-Tat reciprocity. ASTRA operates in three stages: (1) interpreting counterpart behavior, (2) optimizing counteroffers via a tool-integrated action with a linear programming (LP) solver, and (3) selecting offers based on strategy assessment and the partner's acceptance probability. Through simulations and human evaluations, our agent effectively adapts to an opponent's shifting stance and achieves favorable outcomes through enhanced adaptability and strategic reasoning. Beyond enhancing negotiation performance, it also serves as a powerful coaching tool, offering interpretable strategic feedback and optimal offer recommendations beyond human bounded rationality, with its potential further validated through human evaluation.