Rides on Los Angeles shared vehicles are falling 10% month-over-month. Build a diagnostic and action plan: (a) Decompose the decline into acquisition (new riders), activation, cohort retention, and supply constraints using cohort tables and time-of-day/geo cuts; list the exact plots/queries you would run and what each would prove or falsify. (b) Enumerate plausible root causes (seasonality, price/ETA shifts, ops outages, competitor entry) and the minimal data to refute each. (c) For a '$100/month unlimited after a 1-week free trial' offer, decide who should receive the trial (new users, churn-risk users, high-propensity payers) and why; define targeting rules. (d) Provide the break-even formula for the trial: incremental LTV × conversion − CAC − variable costs − fraud loss ≥ 0; solve for the minimum conversion rate given inputs. (e) Outline the A/B test design (unit, duration, sample size, stratification), guardrails (support load, refund rate, fraud), and success criteria for a 4-week run.