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Beyond a traditional stimuli-responsive soft actuator that shows a single motion by a stimulus, multidirectional actuation reversal with a single stimulus is highly required in applications such as shape morphing sensors and soft robotics. Liquid crystal elastomers (LCEs) are one of the most attractive candidates for the soft actuator due to their capability of stimuli-responsive shape changing in 3D, which is programmable with local orientation of LC mesogens. Here, a simple but effective method to fabricate monolithic LCE actuators that are capable of reversible curvature reversal in bending and twisting deformation by a single stimulus-heat-is reported. The curvature reversal of the LCE film can be programmed by means of asymmetric crosslinking density along the thickness and the orientation of the LC mesogens. The curvature reversal of the monolithic LCE film exhibits highly reversible (more than 100 times) and fast actuation (≈3-5 s) by heating and cooling, allowing new concept of a practical application using LCE material: a self-regulated smart valve that is capable of qualitatively sorting liquids by temperature. It is believed that this system is potentially applied to a self-regulated sorting platform for various endothermic and exothermic chemical or biological reactions.