14. Given the function $f ( x ) = \sin \omega x + \cos \omega x ( \omega > 0 ) , x \in \mathbb{R}$. If the function $f ( x )$ is monotonically increasing on the interval $( - \omega , \omega )$, and the graph of $f ( x )$ is symmetric about the line $x = \omega$, then the value of $\omega$ is $\_\_\_\_$.\\
\section*{III. Solution Questions: This section has 6 questions, for a total of 80 points.}