
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 a function $f(x) = \sin \omega x$ where $\omega > 0$, the graph of $f(x)$ is transformed such that all the points on the graph have their y-coordinates unchanged and x-coordinates become $\omega$ times the original value. Then, the resulting graph is shifted to the left by $\frac{π}{2}$ units to obtain the function $g(x)$. Simplified, $g(x) = \_\_\_\_\_\_$. If the function $h(x) = f(g(x)) - 1$ has exactly 4 zeros in the interval $(0, 2\pi)$, what is the range of values for $\omega$?

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