
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 an angle \\(\alpha\\) with its vertex at the origin, its initial side coinciding with the positive half-axis of \\(x\\), and its terminal side passing through point \\(P(-3, \sqrt{3})\\).  
\\((1)\\) Find the value of \\(\sin 2\alpha - \tan \alpha\\);  
\\((2)\\) If the function \\(f(x) = \cos(x-\alpha)\cos\alpha - \sin(x-\alpha)\sin\alpha\\), find the range of the function \\(y = \sqrt{3}f\left(\frac{\pi}{2}-2x\right) - 2f^2(x)\\) in the interval \\(\left[0, \frac{2\pi}{3}\right]\).

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