vertical alignment of 3 columns with different content

vertical alignment of 3 columns with different content

I'm using the linguistic avm library along with tikz and I am trying to
put a \leftrightarrow vertically centered between the attribute-value
matrix and the tikz image.

Thanks in advance for any help.
\begin{figure}[!h]
\begin{minipage}[t]{.40\linewidth}
\vspace{10pt}
\begin{avm}
[{} attra & 1 \\
attrb & 2 \\
attrc & 3 \[\]]
\end{avm}
\end{minipage} \qquad
\fbox{\begin{minipage}[b]{.1\linewidth}
\centering $\leftrightarrow $
\end{minipage}}
\begin{minipage}[t]{.40\linewidth}
\vspace{0pt}
\centering
\begin{tikzpicture}
\node[circle,fill=green,minimum height=30.00pt,minimum
width=150.00pt] {};
\end{tikzpicture}
\end{minipage}
\end{figure}