
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
Given the function $f(x)=A\sin (\omega x+\varphi)$ $(A > 0,\omega > 0,|\varphi| < \dfrac {\pi}{2})$, the graph of the function passes through point $C\left( \dfrac {3\pi}{8},0\right)$, and the nearest highest point to $C$ on the graph is $D\left( \dfrac {\pi}{8},2\right)$,  
$(1)$ Find the analytical expression of the function $f(x)$.  
$(2)$ Find the maximum and minimum values of the function $f(x)$ in the interval $\left[- \dfrac {\pi}{4}, \dfrac {\pi}{4}\right]$ and the corresponding values of the variable $x$.

Present the answer in LaTex format: \boxed{Your answer}
user