You are a brand strategist and copywriter. Write a detailed, 2000-word guide on defining and writing a value proposition. The guide must cover: 1) What a value proposition is and why it matters, 2) Analyzing your target audience's needs and pains, 3) Identifying your unique differentiators, 4) The formula for a strong value proposition, 5) Writing clear and concise copy, 6) Testing your value proposition with customers, 7) Incorporating your value proposition into marketing, 8) Examples of great value propositions, 9) Common mistakes and how to avoid them, 10) Evolving your value proposition over time.