The correct answer is "1 and 3 only" because the Panchayati Raj system is primarily designed to facilitate grassroots democratic governance and promote people's participation in local development through decentralized decision-making. This system empowers local self-governments in villages, ensuring that development initiatives are reflective of the community's needs and aspirations, thus embodying democratic decentralization. While political accountability and financial mobilization are crucial elements of governance, they are more indirect outcomes rather than the fundamental objectives of the Panchayati Raj system itself as framed in its core principles.