How to use group_split() in a way that it adds first row of next group to previous group?

Hey,
I have a dataframe (from a soccer log) I would like to split into groups (based on sequence_id) to later do computations on the groups and save them separately. group_split() would be a great solution for it. My only problem is that I will need the first row of the next group to be included in the previous group because it has information needed for the computations. The last group can either have an extra row with NAs or be empty.

This is a reprex of what I wrote now:

library(dplyr)
data <- tibble(sequence_id = c(1, 1, 1, 1, 1, 1,
                               1, 2, 2, 2, 2, 2, 3, 3, 4, 4, 4,
                               4, 5, 5, 5, 5, 5, 6, 6),
               possession_id = c(1, 1, 1 ,1, 1, 1,
                                 1, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3,
                                 3, 4, 4, 4, 4, 4, 5, 5)
               )

data_split <- data %>% 
  group_split(., sequence_id)

But I would like the output to look like this:

data_split
#> <list_of<
#>   tbl_df<
#>     sequence_id  : double
#>     possession_id: double
#>   >
#> >[6]>
#> [[1]]
#> # A tibble: 8 x 2
#>   sequence_id possession_id
#>         <dbl>         <dbl>
#> 1           1             1
#> 2           1             1
#> 3           1             1
#> 4           1             1
#> 5           1             1
#> 6           1             1
#> 7           1             1
#> 8           2             2
#> 
#> [[2]]
#> # A tibble: 6 x 2
#>   sequence_id possession_id
#>         <dbl>         <dbl>
#> 1           2             2
#> 2           2             2
#> 3           2             2
#> 4           2             2
#> 5           2             2
#> 6           3             2
#> 
#> [[3]]
#> # A tibble: 3x 2
#>   sequence_id possession_id
#>         <dbl>         <dbl>
#> 1           3             2
#> 2           3             2
#> 3           4             3
#> 
#> [[4]]
#> # A tibble: 5 x 2
#>   sequence_id possession_id
#>         <dbl>         <dbl>
#> 1           4             3
#> 2           4             3
#> 3           4             3
#> 4           4             3
#> 5           5             4
#> 
#> [[5]]
#> # A tibble: 6 x 2
#>   sequence_id possession_id
#>         <dbl>         <dbl>
#> 1           5             4
#> 2           5             4
#> 3           5             4
#> 4           5             4
#> 5           5             4
#> 6           6             5
#> 
#> [[6]]
#> # A tibble: 2 x 2
#>   sequence_id possession_id
#>         <dbl>         <dbl>
#> 1           6             5
#> 2           6             5

Does anyone have any tips on how to achieve this? Would lag() help in this case?