Strategic Thinking in a Large-Scale Setting

I'm very good at brainstorming ideas for addressing problems and thinking through the implications of those ideas within my small world. But, I'm not good at dealing with issues in which politically-astute strategic thinking is necessary. This is, in part, because I don't understand the politics and it's also because I just don't like to deal with politics. I find political stuff to just be a time and energy sink that I would rather avoid. I know people who thrive on it - that's not me.

That said, I recently attended a meeting in which a major recommendation was made about restructuring our school. Even after an after-meeting debrief with people who (a) I trust and (b) who understand the politics, I still have no idea what to think. We were asked to provide options and alternatives. I have none (though, I do understand the parameters for the challenge we were handed and that might be useful as it doesn't seem like other people can read those between the lines as well). Mostly, I am just shocked and feeling kind of stupid. I think this is because I know I am good at creative problem solving, but those skills are not enough to even be helpful here.

This highlights for me why I don't want to be in administration. I don't want to have to deal with highly political things in ways that require my strategic thinking because if I make a bad call, my group (program/dept/college/whoever) ends up paying for that. But, I recognize that, in this case, I somehow need to pull myself together enough to be able to evaluate the recommendations that are being drawn up by my colleagues. Maybe when I see the proposal my colleagues create, something will click and the problem-solving part of my brain will just take over?