
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 that the maximum value of $y=a-b\cos3x$ (where $b>0$) is $\frac {3}{2}$, and its minimum value is $-\frac {1}{2}$,

(1) Determine the period and the extremum values of the function $y=-4a\sin(3bx)$ as well as the corresponding set of x-values;
(2) Find the monotonic intervals for the function $f(x)=2\sin(a \frac {π}{3}-2bx)$.

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