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Bramall, 20, came through the ranks at Goodison Park, signing a professional contract in 2017, but was released in the summer.
He impressed manager Steve Kittrick in the pre-season games at Loughborough and Lincoln United.
The signing of striker Smith had already been confirmed prior to the weekend.
Smith played 18 times for Guiseley in National League North last season and has joined on loan.
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