Please don't teach wrong things to foreigner, dude. I think the correct difference of "baca" and "membaca" is: "baca" is more commonly used in command sentences. For example: Read that sign! = Baca tanda itu! "membaca" is more commonly used in complete sentences (subject, verb, object). For example: Father reads newspaper. = Ayah membaca koran.
Correct tense: I have been reading books. Or I have read books. Those tenses are not correct here, in this sentence.
You can't say "a" (singular, tinggal) with "books" (plural, jamak).