Update cart button, custom function

Hey,
Im in need to create custom update button function in the cart. Basically

I need to add additional input (next to quantity) in the cart and depending on the input value i need to change price of the product in the cart.

Where can I modify function which runs after I hit the update cart button?
I mean i need to do some calculations also update some meta for cart items. Closest i’ve found is woocommerce_update_cart_action_cart_updated but it doesnt seem to work – or im doing something wrong.

Thanks in advance