The reaction of 1 mol of 4-methylpenta-1,3-diene with 1 mol of HBr produces a mixture of the following three products: 4-bromo-2-methylpent-2-ene, (E)-4-bromo-4-methylpent-2-ene, and (Z)-4-bromo-4-methylpent-2-ene. Write a mechanism that accounts for the formation of these products.