
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 $$f(x)= \sqrt {3}\sin(\omega x- \frac {\pi}{6})+b$$ (where $\omega>0$), and the minimum distance from the center of symmetry of the graph of the function to the axis of symmetry is $$\frac {\pi}{4}$$, when $$x\in[0, \frac {\pi}{4}]$$, the maximum value of $f(x)$ is 1.  
(I) Find the expression of the function $f(x)$.  
(II) The graph of the function $f(x)$ is translated to the right by $$\frac {\pi}{12}$$ units to obtain the graph of the function $g(x)$. If $g(x)-3\leq m \leq g(x)+3$ holds for all $$x\in[0, \frac {\pi}{3}]$$, find the range of the real number $m$.

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