Pause.
Not every answer to a question needs to be an off-the-cuff quick quip of an answer. When you need time to formulate a cool-headed and considered response — simply pause.
Inserting a few seconds of silence prior to answering a question actually causes the listener to perk up their ears and tune into what you’re going to say next (rather than being in their own head and thinking about how they plan to respond to you).
You may only need to pause a minute to consider your reply, but take longer if you need it.
To expand on your pause, tell people you need to run an errand, or suggest you reconvene after lunch. Have a nice slow cup of hot tea to pass the time, stare out the window, go walk around your building and give yourself time to think.
A pause allows you to not only consider your position, but to also give thought to the words you will use in your response.
There is tremendous power in a pause.
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Give it a try.