
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 $\overrightarrow{a} \parallel \overrightarrow{b}$;

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

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