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Interact."],"published-print":{"date-parts":[[2023,10,31]]},"abstract":"<jats:p>Human\u2013computer integration is an HCI trend in which computational machines can have agency, i.e., take control. Our work focuses on a particular form of integration in which the user and the computational machine share agency over the user's body, that is, can simultaneously (in contrast to a traditional turn-taking approach) control the user's body. The result is a user experience where the agency of the user and the computational machine is so intertwined that it is often no more discernable who contributed what to what extent; we call this \u201cintertwined integration\u201d. Due to the recency of advanced technologies enabling intertwined integration systems, we find that little understanding and documented design knowledge exist. To begin constructing such an understanding, we use three case studies to propose two key dimensions (\u201cawareness of machine's agency\u201d and \u201calignment of machine's agency\u201d) to articulate a design space for intertwined integration systems. We differentiate four roles that computational machines can assume in this design space (angel, butler, influencer, and adversary). Based on our craft knowledge gained through designing such intertwined integration systems, we discuss strategies to help designers create future systems. 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