Mathematical Reasoning Perform rigorous mathematical reasoning and produce publication-quality LaTeX output. Input - — Task type: , , , , , - — Context: equation, theorem statement, problem description, or data description Tasks — Step-by-step equation derivation Show every intermediate step. Justify each with the rule applied. Box final result with . Number important equations with . — Formal theorem proof Use appropriate technique: direct, contradiction, induction, construction, or cases. See for LaTeX templates. — Problem setting formalization Convert informal description into formal mathe…