
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 $f(x)=\sin \omega x+ \sqrt {3}\cos \omega x$ has the smallest positive period of $\pi$, where $x\in \mathbb{R}$, and $\omega > 0$ is a constant.  
$(1)$ Find the value of $\omega$;  
$(2)$ If $f\left( \dfrac {\theta}{2}+ \dfrac {\pi}{12}\right)= \dfrac {6}{5}$, where $\theta\in(0, \dfrac {\pi}{2})$, find $\sin 2\theta$.

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