
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 $$f(x)=2\sqrt{3}\sin x\cos x+2\cos^2 x-1$$ 
(Ⅰ) Find the minimal positive period of the function $f(x)$ and its maximum and minimum values in the interval $[0, \frac{\pi}{2}]$; 
(Ⅱ) If $$f(\alpha)= \frac{6}{5}, \text{ with } \alpha \in \left[\frac{\pi}{4}, \frac{\pi}{2}\right],$$ find the value of $\cos 2\alpha$.

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