
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 $f(x) = \cos^2 \left(\frac{\omega x}{2}\right) + \sqrt{3}\sin \left(\frac{\omega x}{2}\right)\cos \left(\frac{\omega x}{2}\right) - \frac{1}{2}$ ($\omega > 0$), its smallest positive period is $\pi$.
(Ⅰ) Find the value of $\omega$ and the maximum and minimum values of the function $f(x)$;
(Ⅱ) Find the intervals where the function $f(x)$ is monotonically increasing.

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