Switching from fossil fuels to geothermal energy can provide a solution to environmental issues and the energy crisis caused by power and cooling generation systems. In this regard, this study examines an innovative cogeneration system that utilizes low-temperature geothermal energy to generate power and cool the built environment simultaneously. The proposed system incorporates a Kalina-34 cycle, complemented by an integrated absorption refrigeration cycle. System analysis encompasses thermodynamic and exergoeconomic assessments, as well as parametric investigations to gauge the effects of critical parameters on system performance. Following a parametric study, the TOPSIS multicriteria decision-making technique is applied to optimize turbine inlet pressure, vapor generator temperature difference, and ammonia concentration. Finally, the main source of irreversibility is compared by conventional and advanced exergy analyses under optimal conditions. Results show that under optimal conditions, the energy utilization factor (EUF), exergy efficiency, and unit co-generation cost (UCGC) are 11.15 % (30.5 % improvement), 45.54 % (20.1 % improvement), and 6.04 $/GJ (1.63 % reduction), respectively. Furthermore, while conventional exergy analysis prioritizes the improvement of the condenser-1, vapor generator, and turbine in that order, advanced exergy analysis suggests a different priority order, with condenser-1, turbine, and vapor generator being the main objects of improvement, respectively. Implementing this study will significantly improve and optimize the proposed system.