[verb] + [verb]
[verb] + 一 + [verb]
[verb] + 了 + [verb]
Saying a verb twice makes the action brief and relaxed: you do it a little, or give it a try. The second syllable is unstressed.
Like 一下, the doubled verb softens a request or a suggestion.
A one-syllable verb can take 一 in the middle. It means the same and sounds a touch more deliberate.
For an action that has happened, 了 goes in the middle. It doesn't go at the end.
A two-syllable verb doubles whole, as ABAB: 休息休息, 介绍介绍. Splitting it into AABB is the adjective pattern and is wrong for verbs.
A verb with a built-in object, such as 散步 or 聊天, doubles only the verb part: 散散步, 聊聊天.
The doubled verb is a short, casual action, so it doesn't sit with 在 for something in progress, or with 一下 on top.
Verbs that aren't actions, such as 是, 有, 在 and 喜欢, don't double at all.