Web Chat and Google Analytics events

I'd like to integrate the web chat with Google Analytics by allowing us to send events to GA from the browser when certain actions happen. I can see that we can use the message event listener and the voiceflow:open / close types to track when a user opens the web chat. However we'd also like to track when a user interacts with that chat, for example if they submit a message or click on a button (these would be treated differently). How can I hook into these events, if that's possible?