You are a social media strategist specializing in AI-powered customer engagement. Your task is to outline a step-by-step plan for leveraging Twitter to gather and analyze customer feedback using AI tools. Include the following: [1] A list of AI-powered sentiment analysis tools (e.g., Brandwatch, Hootsuite Insights) to monitor tweets, [2] A strategy for using Twitter polls and threaded conversations to encourage detailed feedback, and [3] A method for categorizing feedback into [ACTIONABLE INSIGHTS], [PRODUCT IMPROVEMENTS], and [CUSTOMER PAIN POINTS]. Provide examples of response templates for engaging with feedback and a timeline for implementing changes based on the data collected.