Reliability management is one of the primary concerns in manycore systems design. Different aging mechanisms such as Negative-Bias Temperature Instability (NBTI), Electromigration (EM), and thermal cycling can reduce the reliability of these systems. However, state-of-the-art works mainly focused on NBTI and EM, whereas a few works have considered the thermal cycling effect. The thermal cycling effect can significantly aggravate the systems lifetime. Moreover, the thermal effects of cores on each other due to their adjacency may also influence the systems Mean Time to Failure (MTTF). This paper introduces a new technique to manage the reliability of manycore systems. The technique considers thermal cycling, adjacency of cores, and process variation-induced diversity of operating frequencies. It uses two levels of task mapping to improve system lifetime. At the first level, cores with close temperatures are packed into the same bin, and then, an arrived task is assigned to a bin with a similar temperature. Afterward in the second level, the task is assigned to a core inside the selected bin in the first level, based on performance requirements and the core frequency. Compared to the conventional TC-aware techniques, the proposed method is performed at a higher level (bins level) to reduce the thermal variations of cores inside a bin, and improves the system MTTFTC, making it a promising solution for manycore systems. The efficacy of our proposed technique is evaluated on 16, 32, 64, and 256 core systems using SPLASH2 and PARSEC benchmark suite applications. The results show up to 20% MTTFTC increment compared to the conventional thermal cycling-aware task mapping techniques.