This is the 8111th most frequent Japanese word.
察
"察" means "to perceive," "to infer," or "to assess."
察しました - Inferring or sensing based on context.
彼の態度から何かを察しました。
From his attitude, I inferred something.
察する - To judge or sense based on observation.
察するに、彼は真剣に考えています。
Judging from the context, he is thinking seriously.
察して - To deeply understand or empathize with someone's feelings.