None. State and federal law are separate laws. The federal is over the state law in all cases. That is why cases are heard in the Supreme Court to decide if a state law meets the requirements of the federal consitution. The constitution of the United States is the foundation for all government and law.
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Amending.
They are undefined because the structure and system of their power isn't clearly laid out in the Constitution. The Constitution clearly defines the Presidency, the Congress, and the Judicial system for the federal government. However, those that support the three branches aren't spelled out; this has allowed the three branches to delegate their authority to these groups (whether for good or ill) in order to efficiently improve the functions of government.
Improve the U.S
the purpose was to make the federal government stronger and have more control over the colonists.... etc.
It actually says, "...more perfect Union". Lincoln recognized that the Union was not perfect. The new Constitution was designed with the goal to IMPROVE the Union, making it "more perfect".