I've gathered that と思う means to think about but isn't it a little redundant to add the みたい？
The みたい adds the sense of looking like or seeming but so does 思う so I don't quite understand the combination! Any thoughts?
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You've gotten the みたい part wrong. What you are seeing is a subsidiary verb (～て)みる, which means "to try doing something (and see what happens)". See: What is the difference between "verb＋て＋みる" and "verb＋(よ)う+とする"? みたい meaning "to seem / look like" never follows a te-form.
(very literally) I think I want to try asking them.
I think I'm going to ask them (and see if that can solve our problem).
You may be still wondering if ～たい and と思う are similar and thus redundant, but it's a common way to say one's plan or wish. See: 〜たいと思う -- What does this mean? and Different ways to show intention to do something