Get randomized lists with optionnal seed

Question

I want to random some items in an exercise and be able to display the corresponding solutions in the same order.

With xsim package such lists are in two different places so I thought about a first list to initialize a seed and the second list to use that seed.

I let you this M(N)WE adapted from this answer.

\documentclass{article}
\ExplSyntaxOn
\seq_new:N \l_randomlist_seq
\int_new:N \l_random_items_int
\NewDocumentEnvironment{randomlist}{ o  +b }
{
    % use a regular expression to split the environment
    % around the \item commands
    \regex_split:nnN { \s\c{item}\s } { #2 } \l_randomlist_seq
    \seq_pop_left:NN \l_randomlist_seq \l_items_tl % pop empty first item
    \seq_if_empty:NF \l_randomlist_seq {
        \seq_shuffle:N \l_randomlist_seq %% randonly shuffle items
        % the number of items to print is given by the optional #1
        % defaulting to the full list of items
        \IfNoValueTF{#1}{
            \int_set:Nn \l_random_items_int { \seq_count:N \l_randomlist_seq}
        }{
            \int_set:Nn \l_random_items_int { #1 }
        }
        % finally, insert the enumerate environment
        \begin{enumerate}
            \int_do_while:nNnn \l_random_items_int > 0 {
                \seq_pop:NN \l_randomlist_seq \l_tmpa_tl
                \item \tl_use:N \l_tmpa_tl
                \int_decr:N \l_random_items_int% one less item to go
            }
        \end{enumerate}
    }
}{}
\ExplSyntaxOff
\begin{document}
    This prints four items, it's the exercise
    \begin{randomlist}[4]   %%Generate seed
        \item A
        \item B
        \item C
        \item D
        \item E
    \end{randomlist}
This prints four items it's the solutions of the 
\begin{randomlist}[4]   %%Set seed to match the exercise seed.
    \item soltn A
    \item Soltn B
    \item Soltn C
    \item Soltn D
    \item Soltn E
\end{randomlist}

This prints all items

\begin{randomlist}
    \item soltn A
    \item Soltn B
    \item Soltn C
    \item Soltn D
    \item Soltn E
\end{randomlist}
\end{document}

Addendum :

I've tried to set the seed with \sys_gset_rand_seed the lists are now fixed but don't match each other. i.e. the elements of the exercise part are not in the same order than the solution part with same number of elements.

\documentclass{article}
\ExplSyntaxOn
\seq_new:N \l_randomlist_seq
\int_new:N \l_random_items_int
\sys_gset_rand_seed:n {354}     %%% Despite the seed was set, the lists don't match.
\NewDocumentEnvironment{randomlist}{ o  +b }
{
    % use a regular expression to split the environment
    % around the \item commands
    \seq_set_split:Nnn \l_randomlist_seq { \item } {#2}
    \seq_pop_left:NN \l_randomlist_seq \l_items_tl % pop empty first item
    \seq_if_empty:NF \l_randomlist_seq {
        \seq_shuffle:N \l_randomlist_seq %% randonly shuffle items
        % the number of items to print is given by the optional #1
        % defaulting to the full list of items
        \IfNoValueTF{#1}{
            \int_set:Nn \l_random_items_int { \seq_count:N \l_randomlist_seq}
        }{
            \int_set:Nn \l_random_items_int { #1 }
        }
        % finally, insert the enumerate environment
        \begin{enumerate}
            \int_do_while:nNnn \l_random_items_int > 0 {
                \seq_pop:NN \l_randomlist_seq \l_tmpa_tl
                \item \tl_use:N \l_tmpa_tl
                \int_decr:N \l_random_items_int% one less item to go
            }
        \end{enumerate}
    }
}{}
\ExplSyntaxOff
\begin{document}
    This prints four items, it's the exercise
    \begin{randomlist}[4] %%Generate seed
        \item A
        \item B
        \item C
        \item D
        \item E
    \end{randomlist}
This prints four items it's the solutions of the 
\begin{randomlist}[4]   %%Set seed to match the exercise seed.
    \item Soltn A
    \item Soltn B
    \item Soltn C
    \item Soltn D
    \item Soltn E
\end{randomlist}

This prints all items in a different order than the two previous one
\begin{randomlist}
    \item Soltn A
    \item Soltn B
    \item Soltn C
    \item Soltn D
    \item Soltn E
\end{randomlist}

\end{document}