a. 2-Bromo-3-phenylbutane reacts with $\ce{NaOMe}$ in methanol. What is the mechanism?
b. This compound then reacted with $\ce{CN-}$ in DMSO. What is the mechanism?
My Attempt
a. I am debating between $\mathrm{E1}$ and $\mathrm{S_N1}$ since it is a polar protic solvent and the carbocation can be stabilized by the tertiary carbon and phenyl group. I am leaning towards $\mathrm{E1}$ since $\ce{OMe-}$ is a strong base. Am I correct?
b. If the answer to the first question was $\mathrm{E1}$, then 2-phenylbut-2-ene would be the product. I don't see how that would react with $\ce{CN-}$ in DMSO. So, would no reaction occur?