Why did progressives believe that strong government action was the only way to tackle the social and economic problems of industrialization?

The problem was that, through unfettered capitalism, industrialization had led to an underclass of people who had little-to-nothing in the way of financial and social resources. The main thrust of progressivism was that governmental action could help make sure that those without could be lifted up to where they were able to survive, thrive, and be productive members of society.

You 2

productive most commonly means: achieving or producing a significant amount or result.

explanation:

productive can also mean:

producing or giving rise torelating to or engaged in the production of goods, crops, or other commodities.

these depend on how the word productive is used. most likely productive will mean   achieving or producing a significant amount or result.