$(25$ points$)$ Polycyclic, polyether marine natural products $($secondary metabolites$)$ display a wide range of biological activities. The structure of a natural product from this class, Brevetoxin B$,$ is shown below.

In an attempt to develop a synthetic methodology that would enable the syntheses of such ladder polyether natural products, Jamison and co$-$workers from Massachusetts Institute of Technology discovered a new cascade reaction $($shown below$)$ and disclosed their findings in Science magazine in $2007($Science $2007,317,1189).$ Propose a plausible mechanism for this transformation. Please use curved arrows in your mechanism.