
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 $y=a-b\cos 2x$ $(b > 0)$ is $\frac{3}{2}$ and the minimum value is $-\frac{1}{2}$, find the period, maximum value, and the set of $x$ values for which the function $y=-4a\sin (3bx+\frac{\pi }{3})$ attains its maximum value.

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