Does the taste of food reaching the mouth during belching, followed by swallowing the saliva, affect the validity of the fast and prayer?

If someone burped and tasted food without anything reaching their mouth, then there is no issue, and their fast is valid. However, if some food exited to their mouth due to burping, and they swallowed it despite being able to expel it, their fast is broken. If this happens during prayer, then if they did not intentionally swallow what came out to their mouth, despite being able to expel it, their prayer is valid; otherwise, it is nullified.