This paper introduces a novel automated system for generating architecture schematic designs aimed at streamlining complex decision-making at the multifamily real estate development project's outset. Leveraging the combined strengths of generative AI (neuro reasoning) and mathematical program solvers (symbolic reasoning), the method addresses both the reliance on expert insights and technical challenges in architectural schematic design. To address the large-scale and interconnected nature of design decisions needed for designing a whole building, we proposed a novel sequential neuro-symbolic reasoning approach, emulating traditional architecture design processes from initial concept to detailed layout. To remove the need to hand-craft a cost function to approximate the desired objectives, we propose a solution that uses neuro reasoning to generate constraints and cost functions that the symbolic solvers can use to solve. We also incorporate feedback loops for each design stage to ensure a tight integration between neuro and symbolic reasoning. Developed using GPT-4 without further training, our method's effectiveness is validated through comparative studies with real-world buildings. Our method can generate various building designs in accordance with the understanding of the neighborhood, showcasing its potential to transform the realm of architectural schematic design.