Word family parts for "actively"?

[ELTer]

I had an interesting question in my adult ESL class yesterday. The book talks about word families, and had a chart to fill in with headings of: noun, verb, adjective, and adverb. It gave "actively" as the adverb. What is the root of "actively" - "act" or "active" or...? Also, what would the noun of "actively" be - "act"? If this is so, then what is the verb - "act" or "activate" or something else?... I figured the adjective that goes with "actively" would be "active" but I had trouble working backwards with the students to figure out what the verb and noun would be if the adjective is "active..."

[Hedwig]

Were you supposed to provide only one word for each category. Because I can think of many, and they're all likely to come from the same Latin root.

Noun: act, action, activity, acting, activism, actor
Verb: act, activate
Adj.: active, activated
Adv: actively (and here I'm stumped)

Actively is derived from active, so the noun for actively is probably action.
As to the verb, can't it be associated with both verbs?

[ELTer]

Thanks! Correct- there was only one space for one noun, one verb, and one adjective given the adverb, "actively."

[Tdol]

Does it specify the root? If not, then I'd accept more than one answer as correct.