There are several things you can do but most importantly......
Identify the nature of a claim first- each kind of claim gives rise to an automatic perspective. For example, an extended claim automatically gives rise to a partial agreement/disagreement perspective. A claim that contrasts two things against each other automatically gives rise to a 'synthesis' claim and each qualified claim automatically gives rise to its own typical perspective.
In my opinion, once you have identified the nature of a claim, you should go thru a checklist of perspectives and once you have a perspective, it becomes easier to brainstorm for reasons and examples.