You're thinking about energy and entropy in the wrong context you could add energy to ice by removing the heat surrounding it, bus increasing the ice. You don't need to add energy to ice to get it to melt the heat will naturally dissipate.

Here's a great YouTube video that could explain it better than I could: https://youtu.be/DxL2HoqLbyA?si=yH1_vHCpQrhIbsON

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