Two subfigures, two pages, tikz images

Question

I have a large tikz flow diagram that spans multiple pages. I broke it up into an 'a' and 'b' figure. It would be nice if the caption would state 'Figure 1a:' and 'Figure 1b:' automatically (instead of just 'Figure 1:' for both). Also, I would like the references in the text to work automatically as well (as 1a and 1b without have to state 'a' and 'b' explicitly as I did below). I have tried the subfigure and subcaption packages but to no avail. Each should have 1 unique caption. Here is a MWE.

\documentclass{report}
\usepackage{caption,tikz}
\begin{document}

Would like this to automatically be listed as
Figures~\ref{fig1a}a and~\ref{fig1b}b in text and caption.

\begin{figure}
  \begin{tikzpicture}
    \draw (0, 0) -- (10,  0) -- (10,-12) -- (0,-12) -- (0,0);
    \draw (0, 0) -- (10,-12);
    \draw (10,0) -- ( 0,-12);
  \end{tikzpicture}
  \caption{Figure 1a}
  \label{fig1a}
\end{figure}

\begin{figure}
  \ContinuedFloat
  \begin{tikzpicture}
    \draw (0, 0) -- (10,  0) -- (10,-12) -- (0,-12) -- (0,0);
    \draw (0, 0) -- (10,-12);
    \draw (10,0) -- ( 0,-12);
  \end{tikzpicture}
  \caption{Figure 1b}
  \label{fig1b}
\end{figure}

\end{document}

A second question, probably should be a separate question, what should I be using: figure, caption, subfigure, or subcaption? I have read on other threads that all but subcaption are deprecated, but when I use subcaption with the required document class (not included), I get the following.

Package caption Warning: Unsupported document class (or package) detected, (caption) usage of the caption package is not recommended. See the caption package documentation for explanation.

Does my document class need too be updated? Can anyone clear this up? Thanks in advance.

Answer 1

Note that the a and b are already in the labels.

\documentclass{report}
\usepackage{caption,tikz}
\begin{document}

Would like this to automatically be listed as
Figures~\ref{fig1a} and~\ref{fig1b} in text and caption.

\begin{figure}
  \begin{tikzpicture}
    \draw (0, 0) -- (10,  0) -- (10,-12) -- (0,-12) -- (0,0);
    \draw (0, 0) -- (10,-12);
    \draw (10,0) -- ( 0,-12);
  \end{tikzpicture}
  \def\thefigure{\arabic{figure}a}
  \caption{Figure 1a}
  \label{fig1a}
\end{figure}

\begin{figure}
  \ContinuedFloat
  \begin{tikzpicture}
    \draw (0, 0) -- (10,  0) -- (10,-12) -- (0,-12) -- (0,0);
    \draw (0, 0) -- (10,-12);
    \draw (10,0) -- ( 0,-12);
  \end{tikzpicture}
  \def\thefigure{\arabic{figure}b}
  \caption{Figure 1b}
  \label{fig1b}
\end{figure}

\end{document}