perl or shell to sum columns 2-6 into a single column 2, create 3rd column 12 month binned avg

See attached input file.

assuming the file perl file is called aceavg.pl or the shell script file is called aceavg.sh and creates an output file called aceavg.txt and I want to called the the script by either

perl aceavg.pl > aceavg.txt

or

sh aceavg.sh > aceavg.txt

I want to use the input file found at /path/ace.txt and simply do 2 things. 1st, sum columns 2-6 into a single column 2. 2nd, I want to create a 3rd column with 12 month rolling binned averages. So the third column won't start until month 12 since 12 data points are needed so rows 1-11 will only have two columns of data and the 3rd column of data begins from row 12. See input file.
ace.txt