1. Given non-empty sets
$$
\begin{array}{l}
X=\{x \mid a+1 \leqslant x \leqslant 3 a-5\}, \\
Y=\{x \mid 1 \leqslant x \leqslant 16\} .
\end{array}
$$

Then the set of all values of $a$ for which $X \subseteq(X \cap Y)$ holds is $\qquad$
(2006, Fudan University Independent Admission Examination)
Answer: $a \in[0,7]$.