pronoun agreement with indefinite pronouns
The pronoun that follows everyone, everybody, anyone, anybody, someone, somebody, no one, and nobody.
Those words are singular. They take a singular verb: Everyone is ready. For the later pronoun, they / their / them is the standard form: Everyone brought their key. The generic he is outdated. He or she is correct and heavy. Do not use Everyone brought his key unless you mean only men.
Examples
UseEverybody locked their drawer.
UseSomebody left their coat.
AvoidEverybody locked his drawer. (If the group is mixed or unnamed.)