Gaze around phrasal verb spoken language
Used to describe looking around a certain place or area.
As soon as we got off the bus, we gazed around the skyscrapers in New York city in awe.
After gazing around at each of us, the boss starts speaking.
Sitting on the bench in the park, I quietly gaze around.
I gaze around at the scenery the last time before getting on board coming home.
To quickly look at someone or something
If a person "casts around for someone or something", he/she looks around to find something/someone, or search for an idea.
To observe one's activity
Try to look everywhere for someone or something
A prolonged, strong and determined look, especially when one is expressing disapproval or displeasure
It is mostly used in the present tense.