
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
Determine the values of $a$ and $b$ if the graph of the function $f(x) = \sin^2(ax) - \sqrt{3}\sin(ax)\cos(ax) - \frac{1}{2}$ (where $a > 0$) is tangent to the line $y = b$, and the $x$-coordinates of the points of tangency form an arithmetic sequence with a common difference of $\frac{\pi}{2}$. 
(Ⅰ) Find the values of $a$ and $b$;  
(Ⅱ) Determine the intervals where the function $y=f(x)$ is increasing.

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