Find the total number of ordered quadruples $(a, b, c, d)$ of natural numbers not exceeding 6 that satisfy the following condition. [4 points] $$a \leq c \leq d \text{ and } b \leq c \leq d$$
Find the total number of ordered quadruples $(a, b, c, d)$ of natural numbers not exceeding 6 that satisfy the following condition. [4 points]
$$a \leq c \leq d \text{ and } b \leq c \leq d$$