
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 $\overrightarrow{a}=(\sin x,\frac{3}{2})$, $\overrightarrow{b}=(\cos x,-1)$.

$(1).$ When $\overrightarrow{a}\parallel \overrightarrow{b}$, find the value of $2\cos 2x-\sin 2x$;

$(2).$ Find the range of $f(x)=(\overrightarrow{a}+\overrightarrow{b})\otimes \overrightarrow{b}$ on $\left[-\frac{\pi }{2},0\right]$.

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