2 Kings tells of Josiah clearing out the idols after the book was found. 2 Chronicles has him start in his twelfth year. Which came first?

The two books tell it in different orders, and neither explains the other. 2 Chronicles: "in the twelfth year he began to purge Judah and Jerusalem from the high places, the Asherah poles, the engraved images, and the molten images" (34:3), and the book is found in the work on the house that began "in the eighteenth year of his reign, when he had purged the land and the house" (34:8), when "Hilkiah the priest found the book of the LORD’s law given by Moses" (34:14). After the covenant, "Josiah took away all the abominations out of all the countries that belonged to the children of Israel" (34:33). 2 Kings names no eighth or twelfth year of his reign; the year it gives is the eighteenth: "In the eighteenth year of King Josiah, the king sent Shaphan" (2 Kings 22:3), and Hilkiah says, "I have found the book of the law in the LORD’s house" (2 Kings 22:8). It tells the reading and the covenant (2 Kings 23:1-3), and then, verse after verse, what the king took away (2 Kings 23:4-20). Both books tell that the book was found in the eighteenth year, in the work on the LORD's house (2 Kings 22:3-8; 34:8-14), and both tell of a taking away after the covenant (2 Kings 23:4-20; 34:33). These notes set the two tellings side by side and don't say how they fit.