Where can I find an inexpensive SMS service with API and feedback (possibility to receive SMS back)?

Question

API

Hello. For my project, I am looking for a service that will allow not only to receive messages, but also to receive feedback via SMS. That is, a person can send a message to the same sender (with a consistent response), and the sender, in turn, using some protocol, would be able to send a notification to my site (in json, xml or other format).
Have you met such services, please advise.
Thanks in advance.