Google Apps Script formatDate using user's time zone instead of GMT

Google Apps Script formatDate using user's time zone instead of GMT

I have a line that sets the current date and time in a cell:
sheet.getRange(1,1).setValue(new Date());
Then I have a line that creates a formatted date based on that cell's value:
var addedDate = sheet.getRange(1,1).getValue();
var addedTime = Utilities.formatDate(addedDate, "GMT", "hh:mm a");
The resulting addedTime seems to be in the GMT time zone and I need it to
be in the user's time zone. It will usually be US Eastern Time (-0500),
but if I simply subtract 5 hours from the time then that doesn't account
for daylight saving time (-0400).
I checked the documentation for formatDate here:
https://developers.google.com/apps-script/reference/utilities/utilities#formatDate(Date,String,String)
which links to the official Java SimpleDateFormat class documentation
here:
http://docs.oracle.com/javase/6/docs/api/java/text/SimpleDateFormat.html
... but I can't find a list of valid time zones there to replace the GMT
with.