What Happened to the Byzantines?

In the years around the Battle of Khuzidah, many of the smaller territories in Anatolia submit to the Mongols. In 1256 also that you've got the major advance into the Near East by another huge Mongol army led by Hooligu. And so the Byzantines will have been feeling an increased level of pressure. So what do they do with that? They send ambassadors to Nysia and then take them on the most securitous route around Nysia. At every point in the route, they would station strong companies of soldiers, so as to give the impression that the Byzantine Empire was both vast and heavily armored.