What did Peter the Great do to strengthen his authority?

The correct answer is - abolished the boyars.

Peter the Great was not very fond of the situation in which the previous rulers were, where they were heavily dependent on the boyars and also did not had full control of the situation because of them. In order to gain full control and authority in the country Peter the Great decided to abolish the boyars. Instead of the traditional boyar aristocracy, Peter the Great made the state service as the exclusive means of attaining a high position in the bureaucratic system.

The reason why Peter the Great thought that the boyers should be abolished in order for him to strengthen his authority was their influence and power, and he was not wrong. The boyars were the ones that were deciding and controlling the majority of the things in the country. They had very big local influence and power, having their own boyar council as well where they were deciding the politics and economics of the country. Peter the Great did not wanted to be in such a position where other people will decide what should happen in the country and in which manner, as he wanted to be the one that has the only and last say in the matters, so he made his move.