Tax settlement offer above assessed amount?

So I have a question that I'm having difficulty answering via Google. This year the county appraised my property way above value, like everyone else, and I protested as always. Because of the 10% cap with the homestead exemption, the settlement offer is coming in above the assessed value.

Ie, (numbers not real) house was $300k last year, appraised at $400k this year, but the cap left the assessment at $350k, I protested lower and their "offer" is $355k.

If I accept the offer does that allow them to tax me at $355k instead of the $350k cap if I had just left it alone? Or will the appraisal be adjusted to $355k and I'll still pay $350k…meaning the protest saves me nothing anyway.