$($a$)$ Suggest a retrosynthesis using a mechanistic transform for the following

compound. The starting material should retain rings A and $B.$

$($b$)$ Which one of the two retrosynthetic transformations shown will work? Identify

any clearable or non$-$clearable stereocenters.

$($c$)$ During Corey's synthesis of allomone he utilised the ketone shown below.

Outline the retrosynthesis to a monocyclic precursor.