To promote economic growth and strength the government allows private markets to operate but it also - - - them

The correct word would be either "regulates" or "monitors."

Even though the government allows private markets to operate, there are still laws that need to be followed. These laws originate from poor working conditions in American society during the early 20th century. Before these regulations, businesses made individuals work 50-70 hours a week, did not offer bonus pay, and hired child labor. Now, the government works to regulate (monitor) businesses to make sure that these actions don't happen again.

Along with this, government also works to make sure that private markets do not become like a monopoly or trust. If businesses worked together to act as a monopoly/trust, they could manipulate prices and decrease competition. This is why the government is necessary for private markets.