
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 $f(x) = A\sin(\omega x + \phi)$, where $x \in \mathbb{R}$, and $(A > 0, \omega > 0, 0 < \phi < \frac{\pi}{2})$, the period of the function is $\pi$, and one of the lowest points on its graph is $M(\frac{2\pi}{3}, -2)$.
1. Find the analytical expression of $f(x)$.
2. When $x \in [0, \frac{\pi}{12}]$, find the maximum and minimum values of $f(x)$.

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