The compass should have been invented first. The compass was invented in the early Northern Song Dynasty (Northern Song Dynasty: 960-1127), and the wheel typesetting method was invented by Wang Zhen in 1297 AD.
The following information is for reference only:
Wheel typesetting method:
Wang Zhen, courtesy name Boshan, was born in Dongping, Shandong, and was a famous agriculturist in ancient times. The author of "Nongshu" survives. He was skilled in agriculture, mechanics and printing. When he served as Yin of Jingde County, he taught people how to farm mulberry trees, built bridges and roads, applied medicine to save people, and promoted advanced agricultural tools and technologies. In order to print the "Agricultural Book" written by himself, he created a wheel typesetting frame, invented the wheel typesetting method, and wrote an article "Creating Movable Type Printing Calligraphy", leaving precious documents on movable type printing technology for future generations.
Compass:
In the early Northern Song Dynasty, people discovered the artificial magnetization method and used natural magnets to rub steel needles to make compasses. Later, people learned to fix the compass in the azimuth plate and made compass needles.
The compass at that time was still a water compass. As for the dry compass, it did not appear in my country until the Jiajing period of the Ming Dynasty (1522-1566).