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Peep and pop operations can produce invalid outputs when they are performed on an empty or invalid stack. If there are no elements in the stack when a pop operation is performed, it can lead to an underflow error. Similarly, if a peep operation is performed on an empty stack, it can lead to an error. Additionally, if the stack is not properly initialized or if there are errors in the implementation of the peep and pop operations themselves, it can also result in invalid outputs.