
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) = \frac{\sqrt{3}}{2}\sin{2x} - \cos^2{x} + \frac{1}{2}$,  
(Ⅰ) Find the set of $x$ such that $f(x) = 0$;  
(Ⅱ) Find the minimum value of $f(x)$ in the interval $[0, \frac{\pi}{2}]$.

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