
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 $\overrightarrow{a}=(\sin x, \frac{3}{2})$ and $\overrightarrow{b}=(\cos x, -1)$,
(I) find the value of $\tan 2x$ when $\overrightarrow{a}$ is parallel to $\overrightarrow{b}$;
(II) find the range of the function $f(x)=( \overrightarrow{a}+ \overrightarrow{b})\cdot \overrightarrow{b}$ on $\left[-\frac{\pi}{2}, 0\right]$.

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