This is, of course, a matter of opinion. I would argue that the government should do both of these. If it does the first effectively, however, the second should not be necessary.
The government needs to regulate markets to ensure that there is competition. They must not allow mergers, for example, that give one firm a huge amount of market share. Such a firm could raise prices without fear of competition and would also have much less incentive to innovate in ways that would benefit consumers.
If firms do get too big, such as having diversification in too many regulated areas, the government should break them up. This will result in more competition and better prices and service for consumers. A good example of this was the break-up of AT&T in the 1980s. This led to competition in the telephone business and falling prices for long-distance calling.