The Doctor listened some more and leaned back in his seat, finger idly tapping on the table. Not in any sort of repetitive pattern or code, just because he was thinking. Although he did want to test if she knew different sorts of code at some point. He wanted to test how much she knew in general.
"You remember all of that..." The Doctor said as he kept his focus on her. "So do I" he added. He wasn't sure how much he wanted to reveal. At least for the time being. There was a lot the Doctor kept close to himself. Not many of companions knew much about his past, about his home world and its destruction. The more people knew, the more they could use against you, after all.
"And you want to change the system..." he paused, licking his lips briefly. "Admirable. Difficult but not impossible... well, actually I say that. We're here now so it's hardly likely but it does give you time to prepare and time to build. It gives you an advantage, something unpredictable" he added thoughtfully.