Assembly programming is challenging, even for experts. Program synthesis, as an alternative to manual implementation, has the potential to enable both expert and non-expert users to generate programs in an automated fashion. However, current tools and techniques are unable to synthesize assembly programs larger than a few instructions. We present Assuage: ASsembly Synthesis Using A Guided Exploration, which is a parallel interactive assembly synthesizer that engages the user as an active collaborator, enabling synthesis to scale beyond current limits. Using Assuage, users can provide two types of semantically meaningful hints that expedite synthesis and allow for exploration of multiple possibilities simultaneously. Assuage exposes information about the underlying synthesis process using multiple representations to help users guide synthesis. We conducted a within-subjects study with twenty-one participants working on assembly programming tasks. With Assuage, participants with a wide range of expertise were able to achieve signifcantly higher success rates, perceived less subjective workload, and preferred the usefulness and usability of Assuage over a state of the art synthesis tool.