Finding joint pdf of two functions, one min of two geometric functions and other defined based on difference of variables

Question

I'm really stuck on this problem and I have no clue how to proceed right now.

Let $X,Y$ be random geometric variables. Let $Z = min(X,Y)$, and $W = { \left\{ \begin{array}{lll} 0 & \mbox{if } X<Y \\ 1 & \mbox{if } X=Y \\ 2 & \mbox{if } X>Y \end{array} \right. }$

Find the joint pdf of $Z$ and $W$.

I'm not really sure where to go with this problem. Any suggestions for where to start would be greatly appreciated.