Analyze a hypothetical 'OrderProcessor' class that handles validation, database connection, payment gateway interaction, and email notification—all within 2000 lines of code. Describe the step-by-step process to refactor this class into a modular structure adhering to SOLID principles. Specifically, explain how you would apply the Dependency Inversion Principle to decouple the payment logic and the Single Responsibility Principle to separate the notification logic. Do not write code; provide a architectural blueprint and class interaction description.