What can the United States government do to reduce growing income inequality?

There are a number of steps the US government can take to reduce income inequality. However, the Republican party does not view income inequality as a problem in itself. The GOP argues that the free market should not be interfered with and that productive individuals are naturally better paid, with the assumption being that low-income individuals and families are unproductive. Because of political differences, passing laws to address these issues is problematic.
One reason for growing income inequality is uneven educational opportunities. According to the Organization for Economic Cooperation and Development (OECD), the United States ranks 31st in the Program for International Student Assessment (PISA) worldwide ranking. America does have some of the world's finest K–12 schools, but relatively few children attend these excellent institutions. For many children, education means relegation to third-rate urban schools in need of urgent repair. Also, the cost of college is far too high, discouraging low-income students in particular from attending college, thereby maintaining their low-income status and furthering generational poverty. Though scholarships aim to assuage the impact of high tuition costs for exceptional students, kids who attended the aforementioned underfunded schools are also most likely to need financial aid.
The United States can take several steps to improve its educational outcomes. First, it needs to invest more in early-childhood education. Second, it needs to provide school funding to districts on a more even basis. Today, most schools are funded locally, allowing for wealthier regions to have substantially better schools. A college education must be made affordable for all Americans. Several candidates for the presidency have a plan to tackle the college affordability issue.
A second reason for growing income inequality is the low national minimum wage. The current national minimum wage is $7.25 an hour. The minimum wage is seldom adjusted for inflation. The country has had a minimum wage since 1938, but its current $7.25 an hour is inadequate compared to the cost of living. Some cities and states already have a much higher minimum wage. It is unlikely for the minimum wage to be raised, however, because of Republican opposition in the Senate and the White House. A living minimum wage—and one that is adjusted for inflation on a regular basis—would reduce income inequality.
CEO pay, on the other hand, has risen markedly for years. In 2017, the CEO-to-worker compensation ratio was 312-to-1. In 1965, the ratio was just 20-to-1. There is no logical justification for bloated CEO compensation in the United States. The gap between CEOs and employees in other advanced nations is much smaller. One way to deal with this problem is to require companies to publish this data. Companies that do not meet a certain target could then face punitive taxes. This—like a higher minimum wage—has already been implemented in a few places.
Another reason for the extreme income inequality in the United States is a regressive tax structure. America's tax system is far less progressive than those of most other wealthy nations. The recent tax overhaul passed by President Donald Trump only exacerbated this problem.