Reflection is fundamental to how people make sense of everyday life, helping them navigate moments of growth, uncertainty, and change. Yet in HCI, existing frameworks of designing technologies to support reflection remain narrow, emphasizing cognitive, rational problem-solving, and individual self-improvement. We introduce Daoist philosophy as a non-Western lens to broaden this scope and reimagine reflective practices in interactive systems. Combining insights from Daoist literature with semi-structured interviews with 18 Daoist priests, scholars, and practitioners, we identified three key dimensions of everyday reflection: Stillness, Resonance, and Emergence. These dimensions reveal emergent, embodied, relational, and ethically driven qualities often overlooked in HCI research. We articulate their potential to inform alternative frameworks for interactive systems for reflection, advocating a shift from reflection toward reflecting-with, and highlight the potential of Daoism as an epistemological resource for the HCI community.