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To consider or reflect upon something in order to arrive at a solution for of thorough understanding of it. A noun or pronoun can be used between "think" and "through." I don't think you've thought this plan through. We'll have to think through this server issue before we can move on to the next stage of development.
think something through
to run over and try to settle something in one's mind. Let me think this through and call you in the morning. I will think through this matter and get back to you.
Also, think out. Arrive at a thorough understanding of; devise or contrive thoroughly. For example, That answer doesn't work; I don't believe you've thought the problem through, or He thought out a far more efficient method. The first term dates from the early 1900s, the variant from the mid-1800s. Also see think up.
To reason about or reflect on something, considering every detail and consequence: Make sure you think through the consequences before you act. Don't make the decision to quit your job right away—think the matter through.