Very large-scale (VLS) deep learning models are capable of generating meaningful code snippets, yet the performance drops dramatically when the coding task becomes more complex. Although fully neural approaches have been proposed to solve this problem, the value of the application is still limited. In our work, we propose a neuro-symbolic approach that integrates the symbolic natures of programming and the existing neural language models. We divide a programming task into three phases: forming a hierarchical task composed of functions, completing each function, and fulfilling the corner cases. Because each phase can be completed by language models, the coding process can be fully automated. Our contribution is three-fold. Firstly, we show that with little help from humans, VLS language models are capable of completing non-trivial programming tasks. Secondly, we provide a number of empirical insights to create prompt templates that help the language models generate better code. Thirdly, compared to the existing approaches, our work provides a much more practical approach for programmers and researchers to follow. The generated programming project using our fully automated programming approach and part of the ablation study code are available at https://github.com/BiEchi/FAP.