If you want to display your text from slide 4 onward, you need to use <4-> as overlay specification with one of the following commands:
\uncover<4->{text}: when text is not displayed, it still occupies some space.
\only<4->{text} : when text is not displayed, it doesn't occupy any space.
action<4->{text} : works also in math mode.
\documentclass{beamer}
\begin{document}
\begin{frame}
\begin{itemize}[<+(1)->]
\item First item
\item ...
\item An item somewhere in the middle of the list
\item ...
\item Last item
\end{itemize}
\action<4->{Some text to be synchronized with the item in the middle of the list}
\end{frame}
\end{document}
The counter beamerpauses keeps track of the slide number. If you don't want to manually find the slide number, you can access it using the command \thebeamerpauses. Then you can save it somewhere to use it later in the overlay specification:
\documentclass{beamer}
\begin{document}
\newcounter{slidenumber}
\begin{frame}
\begin{itemize}[<+(1)->]
\item First item
\item ...
\item An item somewhere in the middle of the list \setcounter{slidenumber}{\thebeamerpauses}
\item ...
\item Last item
\end{itemize}
\action<\theslidenumber->{Some text to be synchronized with the item in the middle of the list}
\end{frame}
\end{document}
I'm not sure if saving the value in a counter is the right move though.