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Towel manipulation is a crucial step towards more general cloth manipulation. However, folding a towel from an arbitrarily crumpled state and recovering from a failed folding step remain critical challenges in robotics. We propose joint-probability action inference JA-TN, as a way to improve TransporterNet's operational efficiency; to our knowledge, this is the first single data-driven policy to achieve various types of folding from most crumpled states. We present three benchmark domains with a set of shaping tasks and the corresponding oracle policies to facilitate the further development of the field. We also present a simulation-to-reality transfer procedure for vision-based deep learning controllers by processing and augmenting RGB and/or depth images. We also demonstrate JA-TN's ability to integrate with a real camera and a UR3e robot arm, showcasing the method's applicability to real-world tasks.