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You need to just walk up to her and start a general conversation (you have an easy topic, swimming). Then, ask her if she would like to go to a movie or something. If she is willing then get her number directly from her not the brother. Your first time contacting her needs to be a phone call not a text IMO. It will show that you have interested enough in her that you will giver her your undivided attention. If you are shot down dont worry about it.
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