Synthesize coumarin from 4-allyl-2-methoxyphenol (eugenol) I'm trying to figure out how to get the following reaction: (coumarin from eugenol)



My immediate thoughts are


$\ce{OH}$ and $\ce{OCH3}$are bad leaving groups. 
Could I just add $\ce{HI}$ to the $\ce{C10H12O2}$ to convert the methoxy ($\ce{OCH3}$) group to an $\ce{OH}$group? Then, I could add $\ce{Zn}$ to remove the $\ce{OH}$groups?
Or, is there a way to make the methoxy ($\ce{OCH3}$) group into methanol, which would be a better leaving group?
Once the methoxy and hydroxy groups are removed, I'm left with the benzene ring and the attached butene. I would need to add the $\ce{CO2}$ to form the second benzene ring, but I'm not sure how this would be done.
I might be thinking about this all the wrong way. I was thinking that I need to remove the methoxy and hydroxy groups since they're on a benzene ring, and my product's benzene ring doesn't have these groups. Maybe I don't need to get rid of the methoxy and hydroxy groups at all. Maybe I just need to shift the bonds around?
Since no-one has offered an answer I'm going to try but as I have no database access some of this is a bit flaky.


Heat (maybe microwave) to give multiple Claisen rearrangement products then separate to isolate 2-allyl, 6-methoxyphenol. This is the flakiest step.
Hydroborate with oxidative work-up to take the allyl to propionic acid.
Ring close (PTSA, Toluene) 
Reflux over activated MnO2 to introduce double bond.
Treat with BBr3 to remove Me from MeO group
Zn reduction of OH to H