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Adjust rack to top position and preheat oven to 425 degrees. Wash and dry produce.
Trim, peel, and cut carrots on a diagonal into 1-inch-thick pieces. Peel and dice potatoes into ½-inch pieces. (TIP: For speedier spud prep, skip the peeling.) Halve, peel, and thinly slice onion. Trim and thinly slice mushrooms. Peel and mince garlic.