
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 $$f(x)=2\sin^{2}\left(\frac{\pi}{4}+\omega x\right)-\sqrt{3}\cos(2\omega x)-1$$ with $\omega > 0$, find the smallest positive period of $T=\frac{2\pi}{3}$.
(Ⅰ) Determine the value of $\omega$;
(Ⅱ) If the inequality $|f(x)-m|<2$ always holds for $x\in \left[\frac{\pi}{6},\frac{\pi}{2}\right]$, find the range of the real number $m$.

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