Basic concept of grammar simplification:

$($a$)$ Identify the useless variables in $SA|B,AaA|,BbB,CcC|c|.$

$($b$)$ List all possible unit$-$productions in $SA|bB,AB|a,BA|b|.$

$($c$)$ Identify all nullable variables in $SA|AB,AaA|,BbB|b|.$

$($d$)$ Update the production $S$aAB, if we know that both A and $B$ may be nullable.