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The easiest way of solving this, would be to use JavaScript. You need to have all the options available, and with JavaScript you can alter the options based on what's selected. Something like this:

$("#field-1").change(function(){
  if ($(this).val() == 'option_1') {
    var options = '<option value="foo">bar</option>';
    $("#field-2).html(options);
  }
});

The above is merely example code but illustrates the approach. You might need to do some work, in order to get the different options that should be available.