
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 that the vertex of angle $a$ is at the origin, its initial side coincides with the positive half of the $x$-axis, and its terminal side passes 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 $y=\sqrt{3}f(\frac{\pi }{2}-2x)-2{{f}^{2}}(x)$ in the interval $y=\frac{20-10\sin \theta }{\cos \theta }+10$.

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