
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 $f(x)=\sin (ωx- \frac{π}{6})+ \sin (ωx- \frac{π}{2})$, where $0 < ω < 3$. It is known that $f( \frac{π}{6})=0$.

(1) Find $ω$;

(2) Stretch the horizontal coordinates of each point on the graph of the function $y=f(x)$ by a factor of 2 (the vertical coordinates remain unchanged), then shift the resulting graph to the left by $\frac{π}{4}$ units to obtain the graph of the function $y=g(x)$. Find the minimum and maximum values of $g(x)$ on the interval $\[- \frac{π}{4}, \frac{3π}{4}\]$.

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