
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 $$f(x)=4\sin x\sin^{2}\left( \frac {\pi }{4}+ \frac {x}{2}\right)+\cos 2x-1.$$  
(1) Let $\omega > 0$ be a constant. If $$y=f(\omega x)$$ is increasing on the interval $$\left[- \frac {\pi }{2}, \frac {2\pi }{3}\right],$$ find the range of $\omega$.  
(2) Let the set $$A=\left\{x \mid \frac {\pi }{6}\leq x\leq \frac {2\pi }{3}\right\}, B=\left\{x \mid \left[ \frac {1}{2}f(x)\right]^{2}-mf(x)+m^{2}+m-1>0\right\}.$$ If $A \subset B$ always holds, find the range of the real number $m$.

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