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How to redefine a command in terms of its starred variant?

I am writing a lab report for a class. I want to redefine \section so that \section{Analysis} has the same output that \section*{\centering Analysis} would normally have. I tried

\renewcommand{\section}[1]{\section*{\centering #1}}

but this causes an error. I am able to do

\newcommand{\newsection}[1]{\section*{\centering #1}}

to define a new command to do this, but it would be ideal if I could use the same \section command. I've seen several other questions about similar topics, but I don't understand the code so I can't quite adapt it to my example. My code would be something like this:

\documentclass{article}% redefine the command\begin{document}blah blah blah\section{Analysis}blah blah blah\end{document}

Any help (regarding commands or any other aspects of my code that you find inappropriate) is appreciated.


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