verb + 一 + verb or verb + 一下 means an action happens very soon.
for example, 让我想一想。or 让我想一下。 let me think. or let me see. it means let me think a little while. I need think but i just need a second for thinking. another example, 我能看一看(下)你的新手表吗? can I see your new watch? it means I want to see your new watch but I just see it a little while---one second.
but this usage is just for those verbs whose actions can be last. for example, think, see, listen, teach, etc, for these verbs: come, go, die, etc you cant use them like this: verb+一+verb or verb + 一下
normally, in any normal conversation, we always say like this:
让我想一想 我们一起去逛一逛街(逛街:go shopping) etc
if you say 让我想,we can understand but it is really really weird.