Pedestrians are able to anticipate, which gives them an edge in avoiding collisions and navigating in cluttered spaces. However, these capabilities are impaired by digital distraction through smartphones, a growing safety concern. To capture these features, we put forward a continuous agent-based model (dubbed ANDA) hinging on a transparent delineation of a decision-making process, wherein a desired velocity is selected as the optimum of a perceived cost, and a mechanical layer that handles contacts and collisions. Altogether, the model includes less than a dozen parameters, many of which are fit using independent experimental data. The versatility of ANDA is demonstrated by numerical simulations that successfully replicate empirical observations in a very wide range of scenarios. These scenarios vary from collision avoidance involving one, two, or more agents, to collective flow properties in unidirectional and bidirectional settings, and to the dynamics of evacuation through a bottleneck, where contact forces are directly accessible. Remarkably, the model is able to replicate the enhanced chaoticity of the flow observed experimentally in ’smartphone-walking’ pedestrians, by reducing the frequency of decisional updates, replicating the digital distraction effect. The conceptual transparency of the model makes it easy to pinpoint the origin of its current limitations and to clarify the singular position of pedestrian crowds amid active-matter systems.