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I'd suggest actual wood glue, not superglue, and a good clamp or vise.
Place something (piece of plywood, strip of rubber, several layers of shipping cardboard) between the clamp's surface and the wood to prevent leaving marks.
Leave it in there long enough to dry fully (follow directions that come with the glue).
And apply a wood sealant/waterproofer on the whole piece after you're done.
edit; beaten to the punch
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