"Be remembered" and "come into mind" are parallel expressions, but this combination of passive voice and active voice provides a degree of emphasis or even a sense of totality.
I think there's a similar distinction in the Hebrew, although I'm still not very knowledgeable about the verb forms:
וְלֹא תִזָּכַרְנָה הָרִאשֹׁנוֹת וְלֹא תַעֲלֶינָה עַל־לֵֽב
