After targeted instruction designed to improve student conceptual understanding of physics, a significant fraction of students are not able to answer many questions in a consistent manner. Prior research suggests that even those students who demonstrate that they acquired the relevant knowledge and skills (i.e., possess the requisite "mindware") still tend to rely on their intuitively appealing (and often incorrect) ideas. This study aims to provide insights into cognitive mechanisms that may lead to the identified inconsistencies in student reasoning. We present results of an empirical investigation guided by dual process theories of reasoning and accompanying theoretical constructs of cognitive reflection and mindware. Specifically, we proposed a set of hypotheses to establish a link between student abilities to mediate intuitive responses and performance on physics questions that elicit strong intuitive responses. The cognitive reflection test (CRT), developed by cognitive psychologists, was used to measure students' ability to engage in analytic processing in a more productive manner (i.e., cognitive reflection skills). Additionally, we developed a set of screening-target questions in the context of Newton's third law to assess student reasoning approaches in physics. Results suggest that, in the presence of the necessary mindware, those students who possess a higher level of cognitive reflection skills are more likely to (i) arrive at a correct answer on a question that tends to elicit a strong intuitive, but incorrect response; (ii) recognize the need for justifying their answers, even if a correct answer does not require rejecting an intuitively appealing response; and (iii) engage in consistent reasoning.