I usually use XML::XSH2, a wrapper around XML::LibXML, to process XML files. I tried the following:

#!/usr/bin/perl
use warnings;
use strict;

use XML::XSH2;

package XML::XSH2::Map;
our ($path, $value, $v);

package main;

xsh << 'end.';
    open 1.xml ;
    register-namespace am http://www.abc.com/xml/appmanagement ;
end.

my ($replace, $add);
open my $PROP, '<', 'properties' or die $!;
while (<$PROP>) {
    chomp;
    s=^M_([RA])_/?== or next;
    my $action = $1;
    ($path, $value) = split / = /;

    xsh << '    end.';
        $v = //am:name[.=$path]/../am:value ;
        if $v set $v/text() $value ;
    end.
    next if $v;

    $path =~ s=/=/am:=g;
    xsh "set /am:$path '$value'";

}
xsh 'save :f new.xml';
[download]

This was the created file:

I am not sure that is what you exactly need, though. Especially in case of the last two lines of the properties file: the XPath matches 3 different nodes, it is not clear which one you want to modify.