
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 vectors $\overrightarrow{a}=(1,\cos 2x)$ and $\overrightarrow{b}=(\sin 2x, -\sqrt{3})$, and the function $f(x)=(1,\cos 2x)\cdot (\sin 2x, -\sqrt{3})$

(1) If $f(\frac{\theta}{2}+\frac{2\pi}{3})=\frac{6}{5}$, find the value of $\cos 2\theta$;

(2) If $x\in[0,\frac{\pi}{2}]$, find the range of the function $f(x)$.

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