## 1 Introduction  
Attention is a core biological and cognitive mechanism that allows organisms to coordinate their actions by selectively prioritizing relevant sensory information across different modalities. This information includes but is not restricted to peripheral visual and auditory stimuli, allowing individuals to analyze and respond to their environment [1]. Individuals generate, maintain, and coordinate their intentions through attention and alignment on shared goals or topics to achieve mutual understanding. This alignment considers detecting and interpreting non-verbal cues, such as gaze direction, manual pointing, facial expressions, or verbal signals [2]. Joint attention (JA) emerges as a distinctive form of attention coordination, defined as when two or more individuals deliberately focus on a common event, object, or experience, which is usually referred to as the focus of attention (FoA) [3]. Several mechanisms are considered within the frameworks of JA processes, often performed by following the partner's gaze, pointing gestures, or verbal cues, allowing individuals to set up a common frame of reference. As stated by [PERSON] et al. [4], gaze following implies an ability to detect the direction of a partner's gaze and, in response, to orient one's own eyes and head accordingly to infer their intentions. A similar process occurs with pointing gestures, which also serve to direct attention. These mechanisms play an essential role during development: for example, as children acquire JA capabilities, they begin to develop language skills, interpret social signals, and effectively navigate their environment alongside their caregivers [5]. JA has been classified in various ways throughout the literature, reflecting its multifaceted nature and role in social cognition. [PERSON] et al. [6] classify JA into three levels and two types, reflecting increasing complexity and social coordination. The levels are described as follows: (i) Dyadic representation implies a direct eye-to-eye look between two individuals that is necessary for social contact but does not share an external focus. (ii) Shared gaze is achieved when two individuals coordinate their attention with respect to some third-element object and a shared reference point is established. In this case, the individuals are not expected to notice the other's intentionality regarding the shared reference point. Finally, (iii) triadic representation is the most complex level, where individuals focus on the same object and mutually acknowledge each other's attention. Referring to the types, the literature divides JA into responding to joint attention (RJA) and initiating joint attention (IJA) [7; 8; 9]. RJA refers to the ability of an individual to recognize and follow an object or event referred to by another person. This means responding to certain cues. For example, when one individual looks at an object and/or points to it, the viewer directs his or her attention in the indicated direction. IJA is the capacity to turn another person's attention to a specific object or event. Continuing with the previous example, one would point to a far object and look simultaneously at his or her interaction partner to ensure that he or she also noticed it. RJA and IJA are the building blocks of effective communication, allowing an individual to infer the perspective, intention, and subjective state of another person, which is usually understood as intersubjective understanding [10]. One way to maintain JA and make it successful, whether in a shared object-focused activity or a collaborative action, would be that the individuals involved are engaged during the interaction [11]. Engagement goes beyond just paying attention and involves how much participants are mentally, emotionally, and physically involved in the activity. Generally speaking, high engagement is desired since focused work, collaboration, and meaningful exchange only ensue with sufficiently high levels, especially in dynamic and long-lasting activities [12].