Assess students' ability to evaluate and compare proof strategies for olympiad-style inequalities by selecting, applying, and justifying the use of AM-GM, Cauchy-Schwarz, rearrangement, and Jensen's inequality; students should construct complete rigorous proofs, analyze equality cases, exploit symmetry and homogenization, convert between forms, explain why particular approaches succeed or fail, and compare methods in terms of sharpness, generality, and elegance. Items may require choosing the best approach for a given inequality, producing alternative proofs, and critiquing sample solutions. Level: advanced high school (grades 9–12). Cognitive goal: evaluate reasoning, method selection, and proof quality.