Human judgments and decisions are prone to errors in reasoning caused by factors such as personal biases and external misinformation. We explore the possibility of enhanced reasoning by implementing a wearable AI system as a human symbiotic counterpart. We present "Wearable Reasoner", a proof-of-concept wearable system capable of analyzing if an argument is stated with supporting evidence or not. We explore the impact of argumentation mining and explainability of the AI feedback on the user through an experimental study of verbal statement evaluation tasks. The results demonstrate that the device with explainable feedback is effective in enhancing rationality by helping users differentiate between statements supported by evidence and without. When assisted by an AI system with explainable feedback, users significantly consider claims supported by evidence more reasonable and agree more with them compared to those without. Qualitative interviews demonstrate users' internal processes of reflection and integration of the new information in their judgment and decision making, emphasizing improved evaluation of presented arguments.