
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
The amplitude of the function $f(x) = A\sin(\omega x + \frac{\pi}{3})$ (where $A > 0$, $\omega > 0$) is $2$, and its period is $\pi$.
(1) Find the explicit formula for $f(x)$;
(2) Determine the intervals on which $f(x)$ is monotonically increasing;
(3) Find the range of $f(x)$ on the interval $\left[-\frac{\pi}{2}, 0\right]$.

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