
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 $f(x)=A\sin(\omega x+\phi)$ ($A > 0$, $\omega > 0$, $0 < \phi < \frac{\pi}{2}$), the graph intersects with the x-axis such that the distance between any two adjacent intersection points is $\frac{\pi}{2}$. Furthermore, a lowest point on the graph is given as $M(\frac{2\pi}{3}, -2)$.

(1) Find the explicit expression and period of $f(x)$.

(2) When $x \in \left[\frac{\pi}{12}, \frac{\pi}{2}\right]$, find the range of $f(x)$.

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