"ακολούθησε" is imperative form of the verb "ακολουθώ" and "με" is weak form of the personal pronoun "εμένα" (accusative case).
When a verb in imperative takes tonos on the third syllable from the end, and it is followed by a pronoun, then it takes extra tonos on the last syllable.
"φόρεσέ το" = wear it
"φώναξέ την" = call her
"αφήσέ με" = leave me
Extra tonos helps us to pronounce the verb and the pronoun as one word, without a pause between them.
(Notice that in Imperative Form the weak form of the pronoun goes always after the verb.)