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more like contemplating rather chanting.
origination or dependent arising, Pratītyasamutpāda. He told Ananda he would contemplate, recite Pratītyasamutpāda when he was alone.
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During his developmental years (before he became Enlightened) he might have. This is because mantras are a way for you to match vibration with a particular deity and thus receive their assistance.
The Buddha gave many such great mantras including the Zhunti mantra but a Buddha has no reason to use them because the Buddhas are all connected simultaneously through their uncovered dharmakaya/Tathagatagarba/Buddha-nature.