Is “Did Zheng Wengong, seeing Qi's power, request an alliance, and later first pay court to Chu and participate in the Yu meeting?” true?

The Records of the Grand Historian, 'Hereditary House of Chu', records that in the 33rd year of King Cheng of Chu, Duke Xiang of Song summoned Chu to participate in a meeting: 'So he went, and arrived at Yu, where he was seized and humiliated by the Duke of Song'; and in the 34th year, 'Zheng Wengong paid court to Chu in the south'. The Chronicles of the Eastern Zhou Kingdoms, chapter 34, also describes the King of Chu inviting the feudal lords to Yu: 'The five lords of Chen, Cai, Zheng, Xu, and Cao all came to the meeting at Yu, and together with Duke Xi of Lu, there were six, gathered in one place to discuss. Zheng Wengong spoke first, wishing to honor the King of Chu as the leader of the alliance.' Both records reflect the historical fact that Zheng Wengong paid court to Chu and participated in the Yu meeting during the struggle for hegemony between Qi and Chu.