I'm not sure I can do this - I have read all the stuff about putting a big stop sign in your mind when you think of the OW etc but everything he does I am thinking "yeah great but you've slept with and been in love with another W!!!" I know it is early days but how does this go away and how do you want them to be any where near you ever again?
I think it all depends on whether they're being HONEST with you, and there really is no contact, but they're just struggling with withdrawal from OP; or,
They're LYING to you, and still in contact.
The types of things I would advise someone to do is DRAMATICALLY DIFFERENT in each case, which is why I'm such a strong proponent of "trust, but verify." Once you know for sure, you don't have to keep verifying, but at this stage, how can you even decide how to proceed without knowing if he's just b.s.'ing you with flowers and jewelry, or if these are sincere attempts to speak your LL and help you heal from his infidelity?