Procedural text understanding is a challenging language reasoning task that requires models to track entity states across the development of a narrative. A complete procedural understanding solution should combine three core aspects: local and global views of the inputs, and global view of outputs. Prior methods considered a subset of these aspects, resulting in either low precision or low recall. In this paper, we propose Coalescing Global and Local Information (CGLI), a new model that builds entity- and timestep-aware input representations (local input) considering the whole context (global input), and we jointly model the entity states with a structured prediction objective (global output). Thus, CGLI simultaneously optimizes for both precision and recall. We extend CGLI with additional output layers and integrate it into a story reasoning framework. Extensive experiments on a popular procedural text understanding dataset show that our model achieves state-of-the-art results; experiments on a story reasoning benchmark show the positive impact of our model on downstream reasoning.