Example:
Great bear has head slammer and heavy cannon with momentum.
Great bear advance from avenging force in maintenance phase, hit enemy model with heavy cannon and slam that model for example 3". Slammed model is not boxed after slam is resolved.
Can Great bear move from follow up 3"?
I think that he can, because there is no information in follow up when he can advance.
Both Follow Up and Grand Slam work outside of activation, because neither rule says “during your activation” or anything of that nature. 
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