How to remove a particular repeating element after the first from a character vector

I have a vector of path steps and there's one particular path step that if it repeats I want to eliminate the repetitions.

For example,

my_vec = "A > A > X > B > X > X > X > C > C"

Now if 'X' repeats, then I want to eliminate all repetitions of X besides the first one, while preserving the order of the rest of the elements, such that my desired outcome is:

my_vec = "A > A > X > B > X > C > C", where the repetitive X's are eliminated from the middle.

I tried this with a for-loop and if-else combination, such that I would detect if a previous element in the vector also contains 'X', then replace the element with NA and afterwards I could remove the NA items, but this approach does not provide the desired outcome.

I tried looking here and here, but these just filter out the unique elements, while I want to perform this action on a particular element.

Here's my code:

my_vec <- unlist(str_split(my_vec, '>') )

for (i in length(my_vec)){
if (grepl('X', my_vec[i]) & grepl('X', my_vec[i-1])) {
    steps[i] <- NA

} else {
    next()
}}
my_new_vec <- str_c(steps, collapse = '>')

However, the output is exactly the same as input and nothing is changed into NA.