How would I go about checking if a part collides with another part, and moving it so it doesn't?

I am making a sandbox building game, however I have encountered a problem. When I built, the parts clip through each other. See screenshot to see what I mean. https://imgur.com/a/zajPc1S

local Players = game:GetService("Players")
 
local localPlayer = Players.LocalPlayer
local backpack = localPlayer:WaitForChild("Backpack")
 
local tool = Instance.new("Tool")
tool.RequiresHandle = false
tool.CanBeDropped = false 
tool.Parent = backpack
tool.Name = "Part"

function round(n)
	return math.floor(n + 0.5)
end

tool.Equipped:Connect(function(mouse)
	mouse.Button1Down:Connect(function()
		if mouse.Target and mouse.Target.Parent then
			
			local part = Instance.new("Part", workspace)
			part.Size = Vector3.new(2,2,2)
			part.Position = mouse.Hit.p
			part.Anchored = true
			
			local x = part.Position.x
			local y = part.Position.y
			local z = part.Position.z
			
			part.Position = Vector3.new(round(x),round(y),round(z))		
		end	
	end)
end)