I know it's easy to think that an employee is blowing up or crying intentionally, but some people just cry or fly off the handle easily. That doesn't mean you should ignore the advice to not let it stop you, but don't hold it against them. Give them a moment and then get moving.
I would go one step further and not only write down what you need to convey for yourself, but also for the employee. Make a list of the issues and expected resolutions in an email, with the employee right there, and send it right away. Repetition is your friend. You will avoid many a misunderstanding that way.
Above all, focus on the resolution as a positive thing, and tell the person you know they can make this change. You may have to say that last through gritted teeth, but do it anyway.
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