Large language models (LLMs) are increasingly used in agentic systems, where reliable planning requires tracking how actions change the world over long horizons. This capability is central to reasoning about actions and change (RAC), which involves checking action executability, updating states, and preserving unaffected facts. However, recent RAC and planning benchmarks show that LLMs still struggle with these basic abilities. Effective neuro-symbolic methods for improving RAC and planning directly over natural language remain underexplored. In this paper, we propose ProRAC (Progression-based Reasoning about Actions and Change), a neuro-symbolic framework that leverages LLMs to tackle RAC and planning problems through an agentic, modular design. Central to ProRAC is a unified framework that operates in two modes: a reasoning mode that sequentially executes actions to validate states and answer queries, and a searching mode that integrates this progression into an A* search guided by a fine-tuned heuristic model to find plans. Extensive evaluations across multiple RAC and planning benchmarks show that ProRAC achieves competitive performance across different model backbones and task types.