
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 $f(x)=2\sqrt{3}\sin^2{x}-\sin\left(2x-\frac{\pi}{3}\right)$,
(Ⅰ) Find the smallest positive period of the function $f(x)$ and the intervals where $f(x)$ is monotonically increasing;
(Ⅱ) Suppose $\alpha\in(0,\pi)$ and $f\left(\frac{\alpha}{2}\right)=\frac{1}{2}+\sqrt{3}$, find the value of $\sin{\alpha}$;
(Ⅲ) If $x\in\left[-\frac{\pi}{2},0\right]$, find the maximum value of the function $f(x)$.

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