With respect to the first part of the sentence you are correct. However, on the second part, you are mistaken. "Checks" here is a noun, and the verb is indeed "provided". According to M-W: one of the meanings of "check", as used here is:
3: one that arrests, limits, or restrains : RESTRAINT
The two parties, of opposing political policies, placed a restraint so that the more extreme ideas did not prevail. No doubt it is an allusion to a common phrase in American politics of "checks and balances", which refers to the different parts of government keeping the others within, preventing one from having excessive amounts of power.