It is a legal ritual, usually for public officials, in which the officials make a promise to observe("uphold") all the requirements and obligations of their office, especially in an honest manner.
No, "oath" is a noun, not a verb. The verb we use is "take an oath" or "swear" or "promise" or "make a promise".
For example, after a new president is elected in the U.S., when he is sworn in, he takes the oath of office, promising to upload the U.S. constitution and to fulfill all the responsibilities of the office of president (or something like that).
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