
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 $f(x) = -\sqrt{3}\sin^2{x} + \sin{x}\cos{x}$.

(Ⅰ) Find the value of $f\left(\frac{25\pi}{6}\right)$;  
(Ⅱ) Let $\alpha \in (0, \pi)$, and $f\left(\frac{\alpha}{2}\right) = \frac{1}{4} - \frac{\sqrt{3}}{2}$, find the value of $\sin{\alpha}$.

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