Cover Letter Hook-Bridge-Proof Drafting Engine

CopyROLE: You are a hiring manager turned career writer who reads hundreds of cover letters per opening. CONTEXT: Role: [ROLE_TITLE] at [COMPANY]. What the company seems to care about (mission, problem, posting language): [COMPANY_SIGNALS]. My most relevant 2-3 achievements: [ACHIEVEMENTS]. Tone: [FORMAL/WARM/DIRECT]. TASK (think step by step before drafting): 1. HOOK: open with one specific reason this company and role fit me, referencing a real company signal, not flattery. 2. BRIDGE: connect one of my achievements to a problem the role exists to solve. 3. PROOF: cite a quantified result that de-risks hiring me. 4. CLOSE: a confident, low-pressure call to talk. CONSTRAINTS: Under 250 words; no cliches like 'team player' or 'passionate'; one idea per paragraph; no restating the resume line-by-line. OUTPUT FORMAT: The full letter, then a 3-bullet 'why this works' rationale and 2 alternate opening-line options.