Peer through (something) verb phrase
Look through something such as a window, the fog, binoculars etc.
I peered through the window to see what they were doing down there.
When I peered through her veil, I saw that she was crying silently.
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.
Try to look everywhere for someone or something
A prolonged, strong and determined look, especially when one is expressing disapproval or displeasure
Try to see better with your eyes partially closed
The verb "peer" should be conjugated according to its tense.