Contrast the theoretical foundations of Utilitarianism (Consequentialism) and Deontology (Duty-based ethics). Explain how Utilitarianism determines the morality of an action based on its outcome, specifically the greatest happiness principle. Contrast this with Deontology's focus on rules, duties, and the categorical imperative as formulated by Kant. Provide a theoretical scenario where these two frameworks would yield conflicting moral verdicts.