Answer:
The Puritans remained within the church, hoping to reform it.
Step-by-step explanation:
The "Puritans" were members of Puritanism. They were Protestants who wanted to reform the Church of England in order to purify it. They believe God gave them such purpose. Their movement was centered on not becoming like the Roman Catholic Church. They wanted the Church of England to remove practices that cannot be found in the Bible.
This is the reason why some of the Puritans remained within the church while others separated from it. Unlike the Pilgrims, the Puritans were non-separatists while the Pilgrims were separatists.