The first step in the formation of acetoacetate in liver mitochondrial matrix, is the enzymatic condensation of two molecules of acetyl-CoA to form acetoacetyl-CoA by __________. Acetoacetyl-CoA then condenses with acetyl-CoA by HMG-CoA synthaseto form β-hydroxy-β-methylglutaryl-CoA (HMG-CoA), which is cleaved to free acetoacetate and acetyl-CoA by ______________.