
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 $f(x) = A\sin(wx + \varphi)$ ($A > 0$, $w > 0$, $0 < \varphi < \frac{\pi}{2}$) has a minimum positive period of $\pi$, and on its graph, a lowest point is $M\left( \frac{2\pi}{3}, -2\right)$  
(1) Find the analytical expression of $f(x)$.  
(2) When $x \in \left[0, \frac{\pi}{2}\right]$, find the range of $f(x)$.

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