Network topology and routing algorithms stand as pivotal decision points that profoundly impact the performance of Network-on-Chip (NoC) systems. As core counts rise, so does the inherent competition for shared resources, spotlighting the critical need for meticulously designed routing algorithms that circumvent deadlocks to ensure optimal network efficiency. This research capitalizes on the Triplet-Base Architecture (TriBA) and its Distributed Minimal Routing Algorithm (DM4T) to overcome the limitations of previous approaches. While DM4T exhibits performance advantages over previous routing algorithms, its deterministic nature and potential for circular dependencies during routing can lead to deadlocks and congestion. Therefore, this work addresses these vulnerabilities while leveraging the performance benefits of TriBA and DM4T. This work introduces a novel approach that merges a proactive deadlock prevention mechanism with Intermediate Adjacent Shortest Path Routing (IASPR). This combination guarantees both deadlock-free and livelock-free routing, ensuring reliable communication within the network. The key to this integration lies in a flow model-based data transfer categorization technique. This technique prevents the formation of circular dependencies. Additionally, it reduces redundant distance calculations during the routing process. By addressing these challenges, the proposed approach achieves improvements in both routing latency and throughput. To rigorously assess the performance of TriBA network topologies under varying configurations, extensive simulations were undertaken. The investigation encompassed both TriBA networks comprising 9 nodes and those with 27 nodes, employing DM4T, IASPR routing algorithms, and the proactive deadlock prevention method. The gem5 simulator, operating under the Garnet 3.0 network model using a standalone protocol for synthetic traffic patterns, was utilized for simulations at high injection rates, spanning diverse synthetic traffic patterns and PARSEC benchmark suite applications. Simulations rigorously quantified the effectiveness of the proposed approach, revealing reductions in average latency 40.17% and 34.05% compared to the lookup table and DM4T, respectively. Additionally, there were notable increases in average throughput of 7.48% and 5.66%.