When you are saying Raw input I take it that you mean the KB.
If you go to agents and then select the knowledge agent you can see that you can add some additional context to it. It already has the transcript and the summary but you could try and play around with it to see if you can make it better. Its used to make the KB aware of previous messages. You could try to do it in another format or maybe with only either the Summary or the Transcript.
Let me know what you find out.