Sequential multi-agent systems built with large language models (LLMs) can automate complex software tasks, but they are hard to trust because errors quietly pass from one stage to the next. We study a traceable and accountable pipeline, meaning a system with clear roles, structured handoffs, and saved records that let us trace who did what at each step and assign blame when things go wrong. Our setting is a Planner -> Executor -> Critic pipeline. We evaluate eight configurations of three state-of-the-art LLMs on three benchmarks and analyze where errors start, how they spread, and how they can be fixed. Our results show: (1) adding a structured, accountable handoff between agents markedly improves accuracy and prevents the failures common in simple pipelines; (2) models have clear role-specific strengths and risks (e.g., steady planning vs. high-variance critiquing), which we quantify with repair and harm rates; and (3) accuracy-cost-latency trade-offs are task-dependent, with heterogeneous pipelines often the most efficient. Overall, we provide a practical, data-driven method for designing, tracing, and debugging reliable, predictable, and accountable multi-agent systems.