Let G $=($V$,$ E$)$ be a graph. Provide an algorithmic strategy that can find

and output exactly two spanning trees of G that do not share any edges, e$.$g$.,$

T$1=($V$,$ E$1),$ T$2=($V$,$ E$2)$ where T$1$ and T$2$ are spanning trees of G and E$1\backslash$cap E$2$

$=,$ if such two spanning trees exist.

Provide your algorithmic strategy using pseudo code or a detailed description in

natural language. Explain why your algorithmic strategy meets the requirement.