Most model checkers provide a useful simulation mode, that allows users to explore the set of possible behaviours by interactively picking at each state which event to execute next. Traditionally this simulation mode can not take into consideration additional temporal logic constraints, such as arbitrary fairness restrictions, substantially reducing its usability for debugging the modelled system behaviour. Similarly, when a specification is false, even if all its counterexamples combined also form a set of behaviours, most model checkers only present one of them to the user, providing little or no mechanism to explore alternatives. In this paper, we present a simple on-the-fly verification technique to allow the user to explore the behaviours that satisfy an arbitrary temporal logic specification, with an interactive process akin to simulation. This technique enables a unified interface for simulating the modelled system and exploring its counterexamples. The technique is formalised in the framework of state/event linear temporal logic and a proof of concept was implemented in an event-based variant of the Electrum framework.