how to create a new column by grouping values in an existing column

How to create a new column with variables low if cyl <6 and "high" if cyl>6 and the rest as NAs?

input

head(mtcars) %>% select(cyl)

                  cyl
Mazda RX4           6
Mazda RX4 Wag       6
Datsun 710          4
Hornet 4 Drive      6
Hornet Sportabout   8
Valiant             6

output

                  cyl  new_column
Mazda RX4           6  NA
Mazda RX4 Wag       6  NA
Datsun 710          4  low
Hornet 4 Drive      6  NA
Hornet Sportabout   8  high
Valiant             6  NA