Make Part look like Section and make Section look like paragraph; but with all the numbering preserved?

Question

So I am trying to write a book summary, a few pages long. Is there any way to make part look just like section, except preserving the Roman numbering for part; and make section look just like paragraph, except preserving the Arabic numbering for section? I tried with the following commands:
letpartsection
defthesection{Roman{section}}
letsectionparagraph
deftheparagraph{arabic{paragraph}}

In some way, it worked for part; but it doesn't work for section, as once let section behave like paragraph, I can't add any numbering to it anymore...
Edit: I also need to make sure numbering of the paragraph-ized section not affected by the section-ized part; i.e., make the section numbers continue regardless of parts

Peter Wilson · Answer

Not sure what it is that you want but why not just use section and paragraph while changing the style of their numbering?
documentclass{article} % ????
usepackage{lipsum}

usepackage{chngcntr} % for changing how counters get incremented
counterwithout{subsection}{section} % continuous subsection numbering
counterwithout{subsubsection}{subsection} % continuous subsubsection numbering
counterwithout{paragraph}{subsubsection} % continuous paragraph numbering

renewcommand{thesection}{Roman{section}}
renewcommand{theparagraph}{arabic{paragraph}}

setcounter{secnumdepth}{4} % number paragraph in document
setcounter{tocdepth}{4}    % put paragraph in ToC

begin{document}
tableofcontents
section{First section}
lipsum[1]
paragraph{First paragraph}
lipsum[2]
paragraph{Second paragraph}
lipsum[2]
section{A section}
lipsum[1]
paragraph{A paragraph}
lipsum[2]
end{document}

In response to your comment I have added code so that paragraph numbering is continuous.

Make Part look like Section and make Section look like paragraph; but with all the numbering preserved?

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