Final answer:
Abolitionists primarily employed the political strategy of forming third parties, such as the Liberty Party, to work within the existing political system to influence anti-slavery policies.
Step-by-step explanation:
During the 19th century, abolitionists employed various strategies to combat slavery, with a primary political strategy involving the formation of third parties such as the Liberty Party in 1840. This movement was led by individuals like James G. Birney who believed that working within the existing political system could effect change. The abolitionists who formed these third parties, like the Liberty Party and later the Free-Soil and Republican parties, did so based on the belief that the U.S. Constitution could and should be interpreted as an anti-slavery document. Therefore, the correct answer to what political strategy did abolitionists primarily employ by forming third parties that advocated laws against slavery is (a) They worked within existing political parties to influence anti-slavery policies.