Ramban and Rav Fish on "La'asot"
וַיְבָרֶךְ אֱלֹהִים אֶת-יוֹם הַשְּׁבִיעִי, וַיְקַדֵּשׁ אֹתוֹ: כִּי בוֹ שָׁבַת מִכָּל-מְלַאכְתּוֹ, אֲשֶׁר-בָּרָא אֱלֹהִים לַעֲשׂוֹתAnd God blessed the seventh day, and hallowed it; because that in it He rested from all His work which God in creating had made.
The famous Ramban on Bereishit 2:3, where he compares each of the six millennia to the six days of creation, states that the basis for this comparison stems from the word לעשות. He starts off this idea when he says (my translation):
The Chavel Ramban quotes the Levush on the Rekanati, who explains this by saying (my translation):ודע כי נכלל עוד במלת "לַעֲשׂוֹת" כי ששת ימי בראשית הם כל ימות עולם כי קיומו יהיה ששת אלפים שנה ...And know that also included in the word "La'asot" is that the six days of Creation encompass all the days of the world because its existence will last six thousand years...
Rav Fish's latest says that this word לעשות hints to ל-תשע"ו, meaning that the entire Creation was a preparation for the year תשע"ו. According to the this Ramban, one can say more simply that all the days of the world will continue to perform their duties in the normal way until the תשע"ו year of the sixth millennium.כי מלת לעשות משמע שיעשו ויפעלו עוד כל ימות העולם את פעולתםFor the word "La'asot" implies that all the days of the world will do and perform their duties further.
(Even though the end of that Ramban gives a explicit Ketz of 5118, that's because he wanted it closer to his time and didn't want to delay it too much, but from the word in the Torah that the Ramban uses to convey this idea, 5776 works perfectly.)
Incidentally, Rav Fish quotes R' Yosef Marciano who says that the statement from the Hagaddah:
can also hint that Kivyachol, HKB"H calculated the Ketz to תשע"ו.