## 8 Conclusions  
In this study, we examined the impact of the RJAS on user engagement, a multidimensional construct encompassing cognitive, emotional, and behavioral involvement during interaction. The participants played the \"Odds and Evens\" turn-taking game against a social robot under two experimental conditions (RJAS Active vs. Inactive). While the user was playing the game, auditory and visual stimuli were introduced to simulate real-world dynamics, testing the robot's ability to detect and follow the user's focus. We used a twofold approach to evaluate the system's impact on the user's engagement during the interaction: using the self-reported measurements from the UES-SF, as well as the UBT, a telemetry system. The UBT system monitored head pose orientation to indicate user distractions and attentional focus during the interaction. Combining self-reports with behavioral data remains relatively rare in HRI research, where engagement is typically measured using either questionnaires or manually coded observations. Taken together, the results demonstrate that the activation of the RJAS led to clear improvements in both behavioral and self-reported indicators of user engagement. The participants in the Active condition were less distracted and reported higher engagement, particularly in terms of attentional focus. While some engagement dimensions remained unaffected, possibly due to limited statistical power, overall, the results support the idea that RJA mechanisms enhance the user's involvement in the interaction. The correlational analyses further suggested a meaningful alignment between the self-reports and observed behavior, and the qualitative feedback reflected these findings, highlighting the robot's perceived attentiveness. Overall, the results consistently indicate that activating the RJAS had a positive effect on user engagement during interaction with the robot. Future research should explore whether the benefits of the RJAS hold over longer interactions and a wider range of tasks, moving beyond short game-based sessions. Enhancing the accuracy of the telemetry system by adding complementary signals, such as eye gaze or facial expressions, could improve how well engagement is detected. Another relevant direction is testing the RJAS in specific user groups, such as children with ASD, where supporting joint engagement and prompting JJA behaviors may have practical value. Lastly, adding real-time engagement monitoring to the robot's control system could make it possible for the robot to respond more effectively when users lose focus, completing the interaction loop between IJA, RJA, and EJA. Conceptualization, [PERSON], [PERSON], J.C.C., and A.C.[PERSON]; methodology, [PERSON] and [PERSON]; software, [PERSON]; validation, [PERSON] and [PERSON]; formal analysis, [PERSON]; investigation, [PERSON]; resources, [PERSON] and [PERSON]; data curation, [PERSON] and [PERSON]; writing--original draft preparation, [PERSON] and [PERSON]; writing--review and editing, [PERSON], [PERSON], [PERSON], and [PERSON]; visualization, [PERSON] and [PERSON]; supervision, J.C.C. and A.C.-G.; project administration, J.C.C. and A.C.[PERSON]G.; funding acquisition, J.C.C. and A.C.-G. All authors have read and agreed to the published version of the manuscript. The research leading to these results has received funding from the following projects: Robots sociales para mitigar la soledad y el aislamiento en mayores (SOROLI), PID2021-123941 OA-100, funded by Agencia Estatal de Investigacion (AEI), Spanish Ministerio de Ciencia e Innovacion. Robots sociales para reducir la brecha digital de las personas mayores (SoRoGap), TED2021-132079B-100, funded by Agencia Estatal de Investigacion (AEI), Spanish Ministerio de Ciencia e Innovacion. Mejora del nivel de madurez tecnologica del robot Mini (MeNiR) PDC2022-133518-I00, funded by MCIN/AEI/10.13039/501100-011033 and by the European Union NextGeneration EU/PRTRTR.