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% Preamble:
\usepackage{varwidth}
% then, instead of minipage, use varwidth
\begin{varwidth}[t]{\linewidth}
\begin{itemize}[nosep,after=\strut]
\item First
\item Second
\end{itemize}
\end{varwidth} \
xxxxxxxxxx
% Preamble:
\usepackage{varwidth}
% then, instead of minipage, use varwidth
\begin{varwidth}[t]{\linewidth}
\begin{itemize}[nosep,after=\strut]
\item First
\item Second
\end{itemize}
\end{varwidth} \