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I think she just wants you to validate her till she finds someone new.
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If for some reason the relationship continues, it will most likely poison it.
Both these quotes sum it up.
Basically you have made her feel like she wasn't good enough for you anymore, that's some long term and potentially irreparable damage you've caused to your relationship.
Best piece of advice I can offer is go no contact, freeze her out for at least a month or two so you do not validate her feelings, let her grieve for the loss of the relationship on her own, as must you - do not be her emotional tampon, she will likely use you to get over you, whilst hindering your own healing process.
Use this time to for self improvement and to understand your motives as to why you cheated on her in the first place, there is no quick fix to infidelity, you can't stick a Band-Aid on a leaking nuclear warhead
After this freeze out, you might get things into a better perspective and understand what you really want out of all of this or you may have decided to move on.
If you want to try again, try approaching her casually like you were are old friends and take it slowly from there, but I'm not gonna tell you that this will be easy. - Whatever happens avoid talking about the breakup, instead remind yourselves of the good times you spent together and build comfort and rapport.
Might sound cheesy but:
"If you love something let it free, if it comes back it was meant to be".