Cognitive Reframing, a core element of Cognitive Behavioral Therapy (CBT), helps individuals reinterpret negative experiences by finding positive meaning. Recent advances in Large Language Models (LLMs) have demonstrated improved performance through reasoning-based strategies. This inspires a promising direction of leveraging the reasoning capabilities of LLMs to improve CBT and mental reframing by simulating the process of critical thinking, potentially enabling more effective recognition, generation, and reframing of cognitive distortions. In this work, we investigate the role of various reasoning methods, including pre-trained reasoning LLMs and augmented reasoning strategies such as CoT and self-consistency in enhancing LLMs' ability to perform cognitive reframing tasks. We find that augmented reasoning methods, even when applied to "outdated" LLMs like GPT-3.5, consistently outperform state-of-the-art pretrained reasoning models on recognizing, generating and reframing unhelpful thoughts.