
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 $f(x)=a-b\cos (2x+ \frac {\pi}{6})$ $(b > 0)$ has a maximum value of $\frac {3}{2}$ and a minimum value of $- \frac {1}{2}$.  
$(1)$ Find the values of $a$ and $b$;  
$(2)$ Find the minimum value of the function $g(x)=-4a\sin (bx- \frac {\pi}{3})$ and determine the set of corresponding $x$ values.

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