I'm inclined to choose "going to" in the example below as it's a plan:
I can't go to the meeting tomorrow. I ________ (look after) my nephews.
"will" is unlikely. "am going to" is more likely, but after "can't" we probably expect "have to".
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"will" is unlikely. "am going to" is more likely, but after "can't" we probably expect "have to".