
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 $f(x) = A \sin(\omega x + \frac{\pi}{3})$, where $A > 0$ and $\omega > 0$. The amplitude of the function is 2, and the period is $\pi$.
1. Find the analytical expression of $f(x)$;
2. Find the interval(s) where $f(x)$ is monotonically increasing;
3. Find the range of $f(x)$ on the interval $[- \frac{\pi}{2}, 0]$.

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