My brother and I have equal power of attorney, which allows us to take care of Mom's finances, real estate and health. Can I act alone?

If you and your brother cannot get along even to DISCUSS this and come to a conclusion, then what a real shame that you are both the POA. No, with your mother only have some MILD cognitive decline, SHE is the one to direct how she wishes the home to be sold. How about you, your brother and your Mother get together and decide what you wish to do. If Mother cannot make a choice between his suggestions (I am assuming he plans to assist her in the sale), and your suggestions then I would say that you should resign and relieve yourself of this. You can be named as now a co-POA but as a trustee who would take over IF/WHEN your brother was also unable to serve. That is to say a "successor POA". Having both of you serve when you are unable to come to a reasonable conclusion is going to make your life VERY miserable. With mild cognitive decline (that was my brother's diagnosis when he made me his POA and Trustee of his Trust) your mother remains in charge to decide what she wishes to direct her POA to do. You cannot act as YOU wish. You can only do that in the event your mother is incapable of decision. So you three need to get together. If you cannot agree then you should resign, or your mother should choose one of you as POA and the other as Successor POA. There is nothing on earth so disturbing to the end of a Senior's life as the siblings trying to go to war with one another.