To meet the requirements for authentication using trusted third parties and session maintenance, SAML (Security Assertion Markup Language) and JWT (JSON Web Token) are the best options. SAML is widely used for single sign-on (SSO) and federated authentication, allowing users to authenticate with an external identity provider (trusted third party). JWT is commonly used for maintaining authenticated sessions across web applications and is well-suited for long-term session management, like the six-month duration mentioned. Together, these solutions meet the requirements for standards-based authentication and long-lasting sessions.