Example 7 There is a sequence of numbers: $1,3,4,7,11,18, \cdots$, starting from the third number, each number is the sum of the two preceding numbers.
(1) What is the remainder when the 1991st number is divided by 6?
(2) Group the above sequence as follows:
$(1),(3,4),(7,11,18), \cdots$,

where the $n$-th group has exactly $n$ numbers. What is the remainder when the sum of the numbers in the 1991st group is divided by 6?
(6th Spring Festival Cup Mathematics Competition)