Which two actions might be taken using only the core types?

The correct choice involves actions specific to the core functionality offered by Puppet's foundational types. Core types like 'package', 'user', and 'file' are designed for managing the essential components of system configuration.

Ensuring a package is installed on a system utilizes the 'package' type, which allows for direct management of software packages through the Puppet manifest. This includes operations such as installing, updating, or removing software, effectively ensuring that the desired state of the package is achieved on the managed nodes.

Managing POSIX groups, while also achievable within Puppet, typically utilizes the 'group' type, which may be considered part of core functionality but does not share the same streamlined relationship as the direct package management.

Creating an instance in AWS and concatenating two file fragments are tasks that go beyond the core types. The former requires a resource type specific to cloud management, while the latter involves more complex file manipulation that may engage additional Puppet functionalities. Thus, the action concerning package management stands out as one that can be accomplished solely using the core types.