Conditioning previous values within groups in R

Question

I'm trying to write a code that will allow me to create a TRUE or FALSE variable within the groups name depending on the value of the earliest record of the column poped of the following data.frame: Thank you guys so much in advance for your help!

 library(tidyverse)   
  name<-c("AAA","AAA","AAA","AAA","AAA","AAA","AAA")
  poped<-c(NA,1,NA,NA,1,NA,NA)
  order<-c(1:7)
  tag<-c("X","Y","X","X","Y","X","X")

>   df
  name order tag poped
1  AAA     1   X    NA
2  AAA     2   Y     1
3  AAA     3   X    NA
4  AAA     4   X    NA
5  AAA     5   Y     1
6  AAA     6   X    NA
7  AAA     7   X    NA

I want to mutate a two new variable named CHECK and POS

CHECK will take on the values

    1= If the closest (above) value where the tag column is Y and poped is 1
    0= If the closest (above) value where the tag column is Y and poped is 0
    2 = If the current row has tag = Y
    NA = Otherwise

POS will take on the value of the closest (above) row number where the tag column is Y and poped is 1, and NA otherwise.

My desired outout will be:

>   df
  name order tag poped CHECK POS                                                            why
1  AAA     1   X    NA    NA  NA                                      There is no previous data
2  AAA     2   Y     1    NA  NA                                                current tag = Y
3  AAA     3   X    NA     1   2 the closest value above where tag=Y is in row 2 and poped is 1
4  AAA     4   X    NA     1   2 the closest value above where tag=Y is in row 2 and poped is 1
5  AAA     5   Y     1    NA  NA                                                current tag = Y
6  AAA     6   X    NA     1   5 the closest value above where tag=Y is in row 5 and poped is 1
7  AAA     7   X    NA     1   5 the closest value above where tag=Y is in row 5 and poped is 1

It will be so much appreciated if you guys could help me out witha solution using tidyverse but I will be open for all posible solutions thank you so much