The speaker presented a custom solution at Zapier's AI Showcase in May 2024, showcasing how to manage inbox and calendar within a single platform using a custom GPT (Generative Pre-trained Transformer) built with Zapier's AI Actions. The system was initially built to help the team summarize emails, respond to emails quicker, and manage calendar events due to their busy schedule. This approach is powerful because of its customization capabilities, allowing users to train the GPT to sound like a specific person or tone, and automate tasks using AI Actions. The speaker demonstrated how this custom GPT can be used to summarize emails, respond to emails, create calendar events, send emails, and even delete calendar events, ultimately saving time in the mornings by providing a quick overview of the day's schedule.