[Olefination]

Hi! This is a bit last minute, but I'm studying for an exam tomorrow, and I have come across the same type of problem in two of the practice exams. I think it's probably an important concept that will show up on tomorrow's exam. Unfortunately I have no idea of what the answer is, even after looking around for hours. Attached are the two problems.

As you can see they are very similar, just the first one has a five-membered ring and the second one is a six-membered ring. The second problem gives a little clue about the product (8 C's, 12 H's, and 2 O's). It has the same number of each atom as the starting material, so I guessed it was a rearrangement of some sort...
I thought it might involve formation of a enolate with the LDA, then protection of the enolate's O with the Me3SiCl. But then I don't know what happens with the heat. (And I presume that the H+/H2O at the end is deprotection..)

If anyone has any idea, please help-- Sorry for the last-minute appeal, but I've been searching for the answer but I'm stuck, and if I don't pass this exam tomorrow (in 10 hrs), I don't get my master's degree!  Thank you!

Edit: Sorry, there should be an O on that top ester, as well!
Edit 2: I came up with a product for the second problem from doing a Ireland-Claisen rearrangement but I'm not sure if it's correct (see attached image). Is the stereochemistry lost in the reaction because of the cleavage of the C-O bond that was coming out of the page?

[Olefination]

Edit: see original post

[discodermolide]

I think the enolate must attack from the same face, i.e. the top face giving a product where the CH₂CO₂H group is up.

[Olefination]

Right, yes! I think that's what the prof is looking for here. I had totally forgotten to think in 3-D about the enolate attack. Thank you!

[Olefination]

I passed the exam and I now possess a master's degree! Thank you again!

[discodermolide]

Congratulations, really well done