Look at it logically. The primary cause of poverty, other than the variety caused by mental conditions, is generally lack of investment in labor efficiency, in economics terms "capital." The average worker in America, for example, benefits from quite a bit of capital. Worst case scenario you go to work in say Walmart. That's even if you come to the table with extremely low amounts of human capital (i.e, education). In walmart you benefit from easy access to food (during a lunch break you can get food served to you in a number of minutes), there are machines that aid you in your work letting you get more done faster, work that would otherwise need to be occurring in many different locations is now centralized into one hub. Result? You get a lot more done faster. Obviously, the owners of Walmart are also taking a huge amount of profit from the improved efficiency, but the worker also benefits. The reason is that with a greater profit margin, there is a greater room for companies to lower prices. With the lowered prices, comes greater quantity demanded. With greater quantity demanded, comes more demand for labor. That ups the price of labor, otherwise known as wages.
So, what will help solve poverty (it won't solve inequality, but actual poverty) is a greater and more even spread of the capital available to workers. What can help this? Globalization. Not necessarily capitalism or socialism, although people must be motivated by capitalism in order for it to work. The more efficiently "stuff" can be moved around the planet, the more it makes sense for companies to take advantage of low labor costs overseas. In order to take advantage of that cheap labor, they have to send capital there, thereby improving those people's productivity, so they in turn can demand more. The vast majority of poverty in the world is caused merely by special gaps meaning that some people are valued more as workers merely because of where they happen to have been born. This will naturally go away as the costs associated with remote labor are reduced due to things like the internet, more efficient transportation, etc.
There's local poverty too, poverty of people living right alongside loads of capital, but all things said this accounts for a very small portion of poverty on the planet. This type of poverty may be a growing pain associated with globalization as capital flows to overseas locations, there is reduced demand for labor in the industrialized nations. However, as the people overseas lower their saturation of poverty to that in developed nations, then this element goes away.
If governments want to lower poverty, there are two steps:
1) Encourage firms to invest in capital.
2) Allow workers EVERYWHERE to make use of that capital.
There's also a third thing, that should be obvious but I won't get into right now:
3) Encourage/allow individuals to invest in education, i.e, human capital.
Once you have this baseline understood by everyone involved, then you can actually discuss whether socialism or capitalism more adequately meets these goals.
EDIT: note, this post is specifically addressing "how to reduce poverty" not "how to increase the average wealth per capita.
You are correct but this increases inequality gap. Which can be destabilizing to economies
Its a tough issue and we in uncharted territory
Also I don't agree that lower prices help the worker. It helps consumers. But I'd rather have job stabilitity than lower prices