Final answer:
The sysadmin role grants permissions to perform any action on the server including full administrative capabilities. The other roles like processadmin, securityadmin, and serveradmin have more specific and limited permissions.
Step-by-step explanation:
The role that grants permissions to perform any action on the server is sysadmin. This is because the sysadmin server role encompasses full administrative permissions across the entire server, allowing a user with this role to perform any and all actions. This includes creating and modifying databases, managing user accounts, setting server-wide configuration options, and more. The other listed roles, such as processadmin, securityadmin, and serveradmin have more limited scopes in terms of the permissions they grant.