Can you share your composition, so that we can troubleshoot it out?
It should work fine even for nested symbols. Can you share a sample which can reproduce this issue?
Here is a demo Dropbox - menuComplete - Copy (2).zip
Note you must click the play button to set the variable SetExecution to 1 so that the drop down menu executes. Also run the debug mode on the browser to see the variable and any errors
The problem with the code is that you are trying to access a symbol "power" from symbol "menu", but "power" symbol is not there inside the "menu" symbol. The "power" symbol is on the stage.
So, if you replace the code
sym.getComposition().getStage().getSymbol("power").play("in"); //We are accessing the "power" symbol from stage symbol
you will resolve the issue.