For Sparta, "great deeds" is mentioned by Xenophon (c. 431 to 354 BC) in Constitution of the Lacedaemonians where he relates this in the context of the young gaining part of their education from the experience of their elders:
Note that in other
states the company usually consists of men of the same age, where
modesty is apt to be conspicuous by its ...
This is too long for a comment, but is certainly not a complete answer. However, with that caveat, Athenaeus of Naucratis certainly wrote about that practice in the Cretan commons in his Deipnosophistae.
Quoting Dosiadas' 4th book on Cretan History, he says:
"... After dinner they are in the habit first of deliberating on public affairs; from that ...