
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 $f(x) = 2\sin(\omega x - \frac{\pi}{6})\cdot\cos\omega x + \frac{1}{2}$ (where $\omega > 0$), its smallest positive period is $\pi$.
(Ⅰ) Find the value of $\omega$;
(Ⅱ) Translate the graph of the function $y=f(x)$ to the left by $\frac{\pi}{6}$ units, then stretch the horizontal coordinates of the obtained graph by 2 times while keeping the vertical coordinates unchanged, to get the graph of the function $g(x)$. Find the zeros of the function $g(x)$ on the interval $[-\pi, \pi]$.

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