Admonish

Etymology

From Old French amonester and ultimately Latin admonere, "to remind, advise, warn," from ad- ("to") plus monere, "to warn, advise" (a relative of "mind" and "monitor"). The English ending shifted to "-ish" by analogy with verbs like abolish. At heart it means to put someone in mind of a duty — half warning, half counsel.

verb · /ad-MON-ish/
To warn or reprove someone gently but firmly.
What it names
The precise verb for a corrective word that is also a caution — pointing out a fault while nudging the person toward doing better.
Example
The coach admonished them to rest properly, warning that skipped recovery would end their season early.
Related idea
Reprimand is a formal, often official rebuke; to admonish is milder and forward-looking, aimed at preventing a repeat.