Cool, evolved stars are the main source of chemical enrichment of the interstellar medium (ISM), and understanding their mass loss and structure offers a unique opportunity to study the cycle of matter in the Universe. Pulsation, convection, and other dynamic processes in cool evolved stars create an atmosphere where molecules and dust can form, including those necessary to the formation of life (e.g.~Carbon-bearing molecules). Understanding the structure and composition of these stars is thus vital to several aspects of stellar astrophysics, ranging from ISM studies to modeling young galaxies and exoplanet research. Recent modeling efforts and increasingly precise observations now reveal that our understanding of cool stars photospheric, chromospheric, and atmospheric structures is limited by inadequate knowledge of the dynamic and chemical processes at work. Here we outline promising scientific opportunities for the next decade. We identify and discuss the following main opportunities: (1) identify and model the physical processes that must be included in current 1D and 3D atmosphere models of cool, evolved stars; (2) refine our understanding of photospheric, chromospheric, and outer atmospheric regions of cool evolved stars, their properties and parameters, through high-resolution spectroscopic observations, and interferometric observations at high angular resolution; (3) include the neglected role of chromospheric activity in the mass loss process of red giant branch and red super giant stars, and understand the role played by their magnetic fields; (4) identify the important shaping mechanisms for planetary nebulae and their relation with the parent asymptotic giant branch stars.
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