Finding how to use "rank" or other similar grouping functions with conditionals in R

I am trying in R to perform a ranking or grouping with the following characteristics:

• The content of the field: "Object" of the following record is equal to the content of the field: "Object"
• The date of the next record is sequential (corresponds to the next day)

Example data:

I am using the following code but the result is not correct:

library(plyr)
ddply(df, .(object), transform, rank = (seq_along(date)))

The expected result is similar to the following table:

I appreciate your help in solving this question.

The ranking groups by "object" and orders by "date". The wanted value is then based on if the gap between the previous row and the current row is greater than 1 day, then the rank is incremented by 1.

df <- data.frame(OBJECT = c("PRODUCT1", "PRODUCT1", "PRODUCT1", "PRODUCT2", "PRODUCT2", "PRODUCT2", "PRODUCT2", "PRODUCT2"),
                 DATE = as.Date(c("2023-02-01", "2023-02-02", "2023-02-21", "2023-02-07", "2023-02-09", "2023-02-10", "2023-02-11", "2023-02-23")))

library(dplyr)

# add the wanted column
df <- df %>%
  group_by(OBJECT) %>%
  arrange(DATE) %>%
  mutate(wanted = cumsum(c(1, diff(DATE) > 1)))

df

|  OBJECT  |    DATE    | wanted |
+----------+------------+--------+
| PRODUCT1 | 2023-02-01 |      1 |
| PRODUCT1 | 2023-02-02 |      1 |
| PRODUCT1 | 2023-02-21 |      2 |
| PRODUCT2 | 2023-02-07 |      1 |
| PRODUCT2 | 2023-02-09 |      2 |
| PRODUCT2 | 2023-02-10 |      2 |
| PRODUCT2 | 2023-02-11 |      2 |
| PRODUCT2 | 2023-02-23 |      3 |