Let $X$ and $Y$ be independent discrete random variables such that $P(X=k) = \frac{1}{3}$ for $k \in \{1, 2, 3\}$ and $P(Y=m) = \frac{1}{2}$ for $m \in \{1, 2\}$. Find $P(X+Y \leq 3 | X \cdot Y \leq 3)$.