The conversational search task aims to enable a user to resolve information needs via natural language dialogue with an agent. In this paper, we aim to develop a conceptual framework of the actions and intents of users and agents explaining how these actions enable the user to explore the search space and resolve their information need. We outline the different actions and intents, before discussing key decision points in the conversation where the agent needs to decide how to steer the conversational search process to a successful and/or satisfactory conclusion. Essentially, this paper provides a conceptualization of the conversational search process between an agent and user, which provides a framework and a starting point for research, development and evaluation of conversational search agents.