
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 $f(x) = 2\sin x (\sqrt{3}\cos x + \sin x) - 2$  
(Ⅰ) If point $P(\sqrt{3}, -1)$ is on the terminal side of angle $\alpha$, find the value of $f(\alpha)$.  
(Ⅱ) If $x \in [0, \frac{\pi}{2}]$, find the maximum and minimum values of $f(x)$.

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