
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
Shift the function $$y=\sin(2x- \frac {\pi}{6})$$ to the right by $$\frac {\pi}{12}$$ units to obtain the graph of $$y=g(x)$$. Given that the range of the function $$y=g(x)$$ on the interval $[a, b]$ (where $b > a$) is $$[- \frac {1}{2}, 1]$$, find the minimum and maximum values of $b-a$.

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