Collaborative Problem Solving (CPS) work in mathematics education are widely recognized for engaging students in cognitively demanding activities that foster Higher-Order Thinking Skills (HOTS), like critical thinking and reasoning. However, connections between design features, CPS processes, and learning outcomes remain complex and not fully understood. To address this, we applied a conjecture-based framework to systematically review 45 empirical studies published between 2010 and 2022, focusing on how specific task designs and CPS processes contribute to HOTS. We used a machine learning tool to prioritize relevant studies and streamline the selection process, ending after a threshold number of consecutive irrelevant articles. Guided by the conjecture-based framework, our analysis highlighted how cognitive processes in CPS function as essential mechanisms of learning and measurable outcomes. Specifically, design features, such as technology-supported exploratory tasks and open-ended problems, encourage reflective discourse and deeper cognitive engagement. We also found that structured group procedures, including clear roles and guided interaction protocols, improve collaboration. Nonetheless, challenges like miscommunication and uneven participation can limit CPS from fully realizing its potential to cultivate HOTS. Overall, these findings underscore the importance of aligning task design with CPS processes and using strategies to address collaboration barriers, particularly those related to communication. Without clear protocols and consistent dialogue, even well-designed CPS tasks can fail to cultivate HOTS. In conclusion, this review offers practical insights for educators and researchers implementing CPS effectively in mathematics education, highlighting that fostering open, structured communication is vital for optimizing both collaborative processes and the development of advanced cognitive skills.