## 2 Related Work  
In multi-party conversations, turn management is a crucial mechanism to ensure smooth interactions. [PERSON] et al. [16] observed that natural conversations are typically well-coordinated, with only one person speaking at a time and minimal overlap. They hypothesized the existence of an implicit mechanism that enables efficient coordination of speaking turns. Subsequent research explored various non-verbal cues that play a role in turn management, including grammar, prosody, gaze, body posture, and gestures [17; 18; 19; 20; 21; 22; 23; 24; 25]. For instance, individuals can predict turn completions and openings based on silence, changes in intonation, speech rate adjustments, or prosodic patterns [18; 19; 20]. [PERSON] et al. [22] discussed the role of gestures in turn management, showing how listeners use gestures to indicate speaking intentions or initiate new turns. [PERSON] et al. [24; 25] emphasized the importance of gaze and head movements in coordinating conversational turns and facilitating information flow. Additionally, [PERSON] et al. [26] demonstrated that combining multiple cues, such as head and mouth movements, can significantly enhance participants' competitiveness in turn-taking. With advancements in technology, interactions have expanded into online and virtual environments (e.g., video conferencing, VR social platforms). Unlike face-to-face communication, these interactions are mediated by technology and thus subject to its limitations. For example, network-induced delays [27], tracking errors in VR avatars [28], and insufficient non-verbal cues such as gaze and facial expressions [6; 29] pose challenges for turn management. Users struggle to accurately perceive or interpret each other's speaking intentions, making it difficult to find appropriate moments to insert themselves into conversations or claim speaking turns [10; 11; 30; 31; 32]. This directly affects participants' equal opportunities to contribute [33], and turn-taking balance is closely tied to communication effectiveness and quality [34; 35]. As some studies have pointed out, the difficulties in managing turn-taking hinder effective workplace meetings [36; 37] and educational activities in virtual settings [5; 38]. To address these challenges, researchers have proposed solutions to supplement or reconstruct non-verbal cues to support turn management in virtual environments. For example, [PERSON] et al. introduced proxemic metaphors to assist turn-taking in multi-party video calls [39], while [PERSON] et al. generated 3D photos with gaze direction to improve engagement and efficiency in online meetings [40]. [PERSON] et al. [41] used additional EMG sensors to capture and reconstruct facial expressions on VR avatars to address the lack of non-verbal cues. [PERSON] et al. [42] suggested designing avatar body language to indicate participants' conversational states, attention, and engagement. [PERSON] et al. [43] utilized visualization of participants' conversational turn-taking in shared VR environments to promote balanced turn allocation. Advances in turn-taking recognition, leveraging behavioral tracking data such as mouth movements [12], head movements [9], breathing patterns [44], gaze behavior [13; 45], and multimodal motion data [15], have spurred efforts to develop intelligent systems capable of understanding turn transitions. [PERSON] et al. [46] envisioned systems that predict the next speaker and display relevant information to enhance communication. Such systems could also benefit social agents for natural conversational interactions [47], provide personalized assistance to users who struggle to interpret non-verbal cues due to platform differences or physical abilities [48], and alert leaders in group discussions to adjust their strategies when others' chances to speak are being limited or suppressed [49]. Despite advancements in VR communication research, the practical application of turn-taking support systems in real-world scenarios remains underexplored.