In an Indian state, communities X and Y have been engaged in a long-standing conflict over issues of co-existence and resource sharing. The tensions have intensified, leading to a demand from both communities for self-administration. What is the BEST resolution to this conflict?

Introduction:
The conflict between communities X and Y demands a strategic approach to promote harmony and shared governance.

Strategies:
1. Dialogue and Mediation: Engage in open discussions to comprehend grievances and negotiate amicable solutions.
2. Power-sharing Mechanisms: Institute systems allowing both communities equitable representation in decision-making processes.
3. Conflict Resolution Mechanisms: Establish legal frameworks or local committees to address disputes impartially.
4. Socio-Economic Development: Implement initiatives fostering economic growth and social harmony.
5. Educational Initiatives: Promote programs cultivating tolerance, cultural understanding, and community integration.
6. Impartial Assessment: Consider an unbiased assessment or referendum to gauge preferences for self-administration.

Conclusion:
A harmonious resolution requires a blend of dialogue, inclusivity, equitable resource distribution, and a commitment to fostering mutual respect and cooperation.