Evaluate a trigonometric function at a specific point after determining its form

The question requires first determining the trigonometric function from given information (graph, period, symmetry conditions) and then evaluating it at a particular input value.

gaokao 2023 Q6 View
Given the function $f ( x ) = \sin ( \omega x + \varphi )$ is monotonically increasing on the interval $\left( \frac { \pi } { 6 } , \frac { 2 \pi } { 3 } \right)$, and the lines $x = \frac { \pi } { 6 }$ and $x = \frac { 2 \pi } { 3 }$ are two axes of symmetry of the graph of $y = f(x)$, then $f \left( - \frac { 5 \pi } { 12 } \right) =$
A. $- \frac { \sqrt { 3 } } { 2 }$
B. $- \frac { 1 } { 2 }$
C. $\frac { 1 } { 2 }$
D. $\frac { \sqrt { 3 } } { 2 }$