How to change the number of items in the Bitrix cart?

Question

1C-Bitrix

There are items in the cart. Removing them from the cart is implemented, but changing the number of products cannot be done. I change using By analogy with deletion, using the default template as an example, I tracked where requests go when the quantity in the field changes. Requests go to: 1. /bitrix/components/bitrix/sale.basket.basket/ajax.php 2. /bitrix/components/bitrix/sale.basket.basket.line/ajax.php 3. /bitrix/components/bitrix /sale.products.gift.basket/ajax.php 4. /bitrix/components/bitrix/sale.products.gift.basket/ajax.php 4 requests in total. The second one changes the number of elements in the cart icon . The first one goes to the script that processes the calculation of the amount and returns the changed values. 3 and 4 - I do not touch requests.
<input type="number">
As a result, I send one request to the first address from the list with Ajax.
Json is returned, but the number in it is not changed
Ajax script:

$(document).on('click','#cart_to_quantity',function(){
        $.ajax({
            url: '/bitrix/components/bitrix/sale.basket.basket/ajax.php',
            type: 'POST',
            dataType: 'json',
            data: $(this).serialize(),
            success: function (result) {
                console.log(result);
                BX.onCustomEvent('OnBasketChange');
            }
        });

        return false;


    });

Submit a request form

<form id="cart_to_quantity">
  <input class="clic_item" type="number" name="basket[QUANTITY__<?=$item['ID']?>]" value="<?=$item['QUANTITY']?>">
<input type="hidden" name="basketAction" value="recalculateAjax"
 <input type="hidden" name="site_template_id" value=" bertonv">
  <input type="hidden" name="site_id" value="s1">
  <input type="hidden" name="sessid" value="<?=$my_func?>">
</form>

These requests were tracked when clicking on the increase or decrease of the product
basket[QUANTITY_407]: 12
lastAppliedDiscounts:
basketAction: recalculateAjax
via_ajax: Y
site_id: s1
site_template_id: bertonv
sessid: 3637c1980b2c166cedf20809a4a5d6c7
I don't send via_ajax: Y - otherwise the parameter is empty, lastDiscounts -Applied is empty , it makes no sense to send it. It is
necessary to record changes and return json already changed . Perhaps there is some way out, make a request using BX or something else. I tried to do it as in the default, but I couldn’t repeat it, it’s not clear how everything happens, there’s probably an easier way <input type="number">