Magento 2 - Change product price and add it to cart

Good morning, I am implementing a controller that pulls out a list of products and adds them to the shopping cart, but when I give a personalized price to the product, it does not respect me and puts the original.

Any ideas on how to solve this, thanks in advance.

This is my code:

            if(count($items)>0)
            {
                $this->cart->truncate();

                foreach ($items as $key => $item) {

                    $price = $item->getItemPrice();
                    $price = $priceHelper->currency($price, false, false);

                    $params = array();
                    $params['qty'] = $item->getItemQuantity();//product quantity
                    $params['price'] = $item->getItemPrice();//product price|
                    $request = new \Magento\Framework\DataObject();
                    $request->setData($params);


                    $_product = $this->_productRepository->getById($item->getItemId(),true,null,true); 

                    $_product->setIsSuperMode(true);
                    $_product->setCustomPrice(20);
                    $_product->setOriginalCustomPrice(20);


                    $_product->setSpecialPrice(120);
                    $_product->setPrice(40); 
                    $_product->save();




                    $this->cart->addProduct($_product, $request);

                }

                try
                {
                    $this->cart->save();
                    $this->messageManager->addSuccessMessage('Cotizacion agregada a carrito correctamente');
                    $resultRedirect->setUrl($this->_redirect->getRefererUrl());
                    return $resultRedirect;
                }
                catch(Exception $e)
                {

                    $this->messageManager->addErrorMessage('Ocurrio un error agregando la cotizacion al carrito');
                    $resultRedirect->setUrl($this->_redirect->getRefererUrl());
                    return $resultRedirect;
                }


            }