
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 $f(x)= \sqrt {2}\sin \left(x- \dfrac {\pi}{12}\right)$, where $x\in\mathbb{R}$  
$(1)$ Calculate the value of $f\left( \dfrac {\pi}{3}\right)$.  
$(2)$ If $\sin \theta= \dfrac {4}{5}$, with $\theta\in\left(0, \dfrac {\pi}{2}\right)$, find the value of $f\left(\theta- \dfrac {\pi}{6}\right)$.

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