
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 $$f(x)=\sin(2\omega x- \frac {\pi}{6})+4\cos^{2}\omega x-2$$, where $\omega>0$, the distance between two adjacent intersections of its graph with the x-axis is $$\frac {\pi}{2}$$.

(Ⅰ) Find the analytical expression of the function $y=f(x)$;  
(Ⅱ) Find the set of values of $x$ for which $f(x) \geq -\frac { \sqrt {3}}{2}$;  
(Ⅲ) If the graph of $f(x)$ is translated to the left by $m$ units ($m>0$) to obtain the graph of function $g(x)$, which exactly passes through the point $(-\frac {\pi}{3}, 0)$, when $m$ takes the minimum value, find the intervals of increase of $g(x)$ on $[-\frac {\pi}{6}, \frac {7\pi}{12}]$.

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