Utilizing waste heat to drive thermodynamic systems is imperative for improving energy efficiency, thereby improving sustainability. A combined cooling and power systems (CCP) utilizes heat from a temperature source to deliver both power and cooling. However, CCP systems utilizing LNG cold energy suffers from low second law efficiency due to significant temperature differences. To address this, an "Advanced Power and Cooling with LNG Utilization (ACPLU)" system is proposed, integrating a cascaded transcritical carbon dioxide (TCO2)-LNG cycle with an Organic Rankine cycle (ORC) for improved power generation and an absorption refrigeration system (ARS) for simultaneous cooling. This study evaluates the second law efficiency, net work output, and exergy destruction performance through a sensitivity analysis, optimizing variables such as heat source temperature, superheater temperature difference, ORC and CO2 turbine inlet and condenser pressures, evaporator temperature, and pinch point temperatures of heat exchangers and generator. Compared to previous studies on CCP systems, the ACPLU shows a superior performance, with a second law efficiency of 27.3 % and a net work output of 11.76 MW. Cyclopentane as an ORC working fluid resulted in the highest second law efficiency of 29.06 % and net work output of 12.27 MW. Parametric analysis suggested that heat source temperature significantly impacts net power output. The exergy analysis concluded that a high-pressure ratio and good thermal match between the heat exchangers enhance overall performance. Utilizing artificial neural network (ANN) to produce a multiple-input-multiple-output (MIMO) objective function and performing multi-objective optimization (MOO) using genetic algorithm (GA), an improved second law efficiency and net power output by 28.11 % and 14.16 MW respectively, with pentane as the working fluid, is demonstrated. An average cost rate of 9.121 $/GJ was observed through a thermo-economic analysis. The ACPLU system is promising for medium temperature waste heat recovery, such as, pharmaceutical manufacturing plants.