Subject to the provisions of section fifteen of this article, every bill passed by the Legislature shall, before it becomes a law, be presented to the governor. If he approves, he shall sign it, and thereupon it shall become a law; but if not, he shall return it, with his objections, to the house in which it originated, which house shall enter the objections at large upon its journal, and may proceed to reconsider the returned bill. Notwithstanding the provisions of section fifty-one, article six of this constitution, any such bill may be reconsidered even if the Legislature is at the time in extended session for the sole purpose of considering the budget bill, as specified in said section fifty-one. If after any such reconsideration, a majority of the members elected to that house agree to pass the bill, it shall be sent, together with the objections of the governor to the other house, by which it may likewise be reconsidered, and if approved by a majority of the members elected to that house, it shall become a law, notwithstanding the objections of the governor. If upon any such reconsideration the bill is amended and reenacted, then it shall be again sent to the governor and he shall act upon it as if it were before him for the first time. In all cases, the vote of each house shall be determined by yeas and nays to be entered on the journal. Any bill which shall not be returned by the governor within five days, Sundays excepted, after it shall have been presented to him shall be a law, in the same manner as if he had signed it, unless the Legislature shall, by adjournment sine die, prevent its return, in which case it shall be filed with his objections in the office of the secretary of state within fifteen days, Sundays excepted, after such adjournment, or become a law.