
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 a function defined on $\mathbb{R}$, $f(x)=2\cos \omega x\sin (\omega x+ \dfrac {\pi}{6})- \dfrac {1}{2}(\omega > 0)$, with a period of $\pi$.  
$(1)$ Find the value of $\omega$ and the intervals where $f(x)$ is increasing;  
$(2)$ Let $g(x)=f(x)+\sin (x- \dfrac {\pi}{6})$, find the range of $g(x)$.

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