Should the united states' executive and legislative branches act to promote and increase global free trade? why or why not?

Yes. the US executive and legislative branches should act to promote and increase global free trade. 

1) The US is pretty much the 'big brother'. Whatever US 'says' usually would affect the world one way or another
2) If free trade was promoted, there would be much more profit, as companies and nations do not have to pay for tolls and such, and 3rd world countries can have a higher GDP.
3) It brings the world a bit more together, introduces different variety of world products to each nation, and can help make it a better world
  3a) People would learn more about the lifestyle of other people around the world, and could find out what they can do to help each other.
  3b) If products fail to arrive, most likely something happened to the countries, so people around the world would know that they need help

hope this helps 

Word of mouth.