Paul R. La Monica / CNN Business:   Microsoft and Amazon, the two most valuable companies in the world, are already competing for supremacy in cloud computing. Now Microsoft has its sights set on battling Amazon in the lucrative health care market as well. Microsoft (MSFT) announced a partnership with Walgreens Boots Alliance (WBA) Tuesday. As part of the deal, Microsoft will become Walgreen’s new cloud provider. The two said they will also work on solutions to lower health care costs. Walgreens will open up 12 “digital health corners” in stores that will sell health care-related gadgets. The two companies said the partnership will help Walgreens gain personalized data about their customers’ health, which will allow pharmacists to give better, customized nutrition and wellness solutions. The Microsoft-Walgreens joint venture appears to be a clear move by the two companies to try and counter Amazon’s (AMZN) growing clout in health care.