How to change select list from another using AJAX in Joomla

I have a list of countries and a list of cities for each country. I set both as drop-down list.

My problem is how can I change the cities listed when the selected country changes?

This is my XML code:

<field name="country_id" type="sql" class="country" label="Country"
       description="Country" required="true"
       query="SELECT id, title FROM #__destination_countries WHERE state = 1"
       key_field="id" value_field="title" filter="raw">
</field> 

<field name="city_id" type="sql"
       query="SELECT id, title FROM #__destination_cities WHERE state = 1"
       key_field="id" value_field="title" class="city" label="City"
       description="City" required="true" filter="raw">
</field> 

Ajax code:

jQuery(document).ready(function($) {
    $(".country").change(function(){
        country_id = $("#" + this.id).val();
        $.ajax({
            url:'index.php?option=com_destination&task=cities.getListCities',
            type: "POST",
            data: {
                'country_id': country_id
            }
        }).done(function(msg) {
            console.log(msg);
            $(".city").html(msg);

        })
    })
});

This is my server-side code

public function getListCities()
{
    $country_id = JRequest::getInt('country_id', 0);
    $model = $this->getModel();
    $model->setState('filter.country_id', $country_id);
    $items = $model->getItems();
    $option = array();
    foreach ($items as $key => $item) {
        $option[] = "<option value='{$item->id}'>{$item->title}</option>";
    }
    $return = implode("", $option);
    echo $return;
    exit;
}

But it did not show as i want, it show like this

<select style="display: none;" required="required" id="jform_city_id" name="jform[city_id]" class="city required chzn-done">
    <option value="1">City 1 of Coutry 1</option>
</select>
<div style="width: 220px;" class="chzn-container chzn-container-active" id="jform_city_id_chzn">
    <a tabindex="-1" href="javascript:void(0)" class="chzn-single chzn-single-with-drop">
        <span>City 1 of Coutry 1</span>
        <div><b></b></div>
    </a>
    <div class="chzn-drop" style="display: block; width: 218px; top: 24px;">
        <div class="chzn-search"><input tabindex="-1" style="width: 183px;" autocomplete="off" type="text"></div>
        <ul class="chzn-results">
            <li id="jform_city_id_chzn_o_0" class="active-result" style="">City 1 of Coutry 1</li>
            <li id="jform_city_id_chzn_o_1" class="active-result result-selected" style="">City 2 of Coutry 1</li>
        </ul>
    </div>
</div>

Just change the select option but did not change the below.

A note apart, you're using the deprecated JRequest::getInt(); where you should be using

$input = JFactory::getApplication()->input;
$country_id = $input->getInt('country_id', 0);

In order to change the second select, you must trigger the update of the second select:

$(".country").change(function(){
    // your ajax call from your code

    // on success, you need to trigger the second select by using
    $(".city_id").val(your_value_from_ajax_response).trigger("liszt:updated");

});