Dynamic Update for 2D Random Walk

I have code for a random walk

pt = Accumulate[{Sin@#, Cos@#} & /@ RandomReal[{0, 2 Pi}, 1000]]; boundary = {Min@pt, Max@pt}; Norm@Last@pt; ListLinePlot[pt, PlotRange -> {boundary, boundary}, AspectRatio -> 1] 

which produces something like this:

Random Walk

I want to try to animate this, so that I can see how the random walk updates step by step with each new coordinate. I tried using DynamicUpdating but I couldn’t really get it to work. Is there any way to achieve this? Any help is extremely appreciated!