function ajax(options) {
      return new Promise(function (resolve, reject) {
        $.ajax(options).done(resolve).fail(reject);
      });
}

then run:

ajax({
    url: YOUR_URL,
    type: 'post',
    dataType: 'json',
    data: {
      action: some_action,
      action_2: another_action
    }
}).then(
    function fulfillHandler(data) {
      // callback
    }
).catch(function errorHandler(error) {
    // error
});