Might not result in any different outcome from the first scenario.Police were notified, reports taken, end result nothing.
...use a small GPS tracker and place it inconspicuously on a easily identifiable item you own. ...notify the proper authorities immediately and how to locate said item.
Guy I know was mugged at gunpoint and one of the items taken was his phone. He used the find my phone app and tracked it to an apartment complex. Told the cops where to find the people that mugged him, and they told him they weren't going to do anything. All depends on your local constabulary...