Problem 304

4. Fill the numbers $1, 2, 3, 4, 5, 6$ into the 6 vertices of the hexagon $A B C D E F$, and let $S_{1}, S_{2}, \cdots, S_{6}$ represent the sums of the numbers at the 3 adjacent vertices $(A, B, C), (B, C, D), \cdots, (F, A, B)$ respectively.
(1) Try to give a way to fill the numbers so that $S_{1}, S_{2}, \cdots, S_{6}$ are all greater than or equal to 9;
(2) Can you find a way to fill the numbers so that $S_{1}, S_{2}, \cdots, S_{6}$ are all greater than or equal to 10? If yes, provide a specific way to fill the numbers; if not, explain the reason.