Think of 'induct' as a formal ceremony or process when someone joins a new group or role. She was inducted into the National Honor Society in a special ceremony.
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Initial Entry
'Induct' often marks the starting point of someone's membership or service in a group. After the election, the mayor-elect will be inducted in January.
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Exclusive Groups
Use 'induct' for instances involving exclusive groups where entry is considered a privilege. The renowned scientist was inducted into the Royal Society.