How can I make `fill-paragraph` on selected text respect indentation in AUCTeX?

Question

Using fill-paragraph in AUCTeX normally respects the given indentation. However, if I use fill-paragraph on a selection, only the first line will be indented, the other lines won't. Is there a way to correct this?

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Example. I have the following LaTeX code

\begin{proposition}
    For every right-angled triangle with side \(a,b\) and \(c\), where \(c\) is the hypotenuse, we have \(a^2 + b^2 = c^2\).
\end{proposition}

If my cursor is on the middle line, and I press M-q (which executes fill-paragraph), then I obtain

\begin{proposition}
    For every right-angled triangle with side \(a,b\) and \(c\), where
    \(c\) is the hypotenuse, we have \(a^2 + b^2 = c^2\).
\end{proposition}

which has the correct indentation. However, if I select the middle line and press M-q, I get

\begin{proposition}
    For every right-angled triangle with side \(a,b\) and \(c\), where
\(c\) is the hypotenuse, we have \(a^2 + b^2 = c^2\).
\end{proposition}

As you see, the indentation of the second line is incorrect.

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I did some more research and experimentation. According to the AUCTeX documentation on Indenting, there is a special LaTeX-fill-region, which does not seem to suffer from my problem. However, when I have selected text, M-q uses fill-region instead of LaTeX-fill-region. How can I change this?