The verb concur means to agree or have the same opinion.
Synonyms are acquiesce, accord, coincide, or jibe.
The word origins from Latin concurrere meaning “to run together, assemble hurriedly, clash, fight”, in transfer use “to happen at the same time”. It comes from the assimilated form of com meaning “together” plus currere meaning “to run”. The sense of “to coincide, happen at the same time” is from 1590s. The meaning “to agree in opinion” is from 1580s in English.
I do concur with your three conditions.
The public opinion does not necessarily concur with the press.
Both teachers decided to concur in this lesson.