[verb AB] + [verb AB]
[verb AB] + 了 + [verb AB]
[adjective AB] + [adjective AB]
A two-syllable verb repeated whole – AB becomes ABAB – means doing it briefly or casually: "a bit", "have a go at". It softens a suggestion or a request the way 一下 does.
The verb has to be something you choose to do. 知道, 是, 喜欢 and 认为 don't double.
A verb doubles as a block. AABB is the pattern for adjectives that describe (高高兴兴, 干干净净), and it means something else.
For something already done, 了 goes between the two halves.
一 can go between a one-syllable verb and its double (看一看), but not between two-syllable ones.
A few adjectives for pleasant states double as ABAB: 高兴, 暖和, 凉快, 热闹, 轻松. They then act like verbs: "let's have a bit of fun", "warm up a bit".
AABB describes; ABAB does. 他高高兴兴地走了 is "he left happily"; 让他高兴高兴 is "let him have some fun".