
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 $\overrightarrow{a}=(\sin x,\cos x)$, $\overrightarrow{b}=( \sqrt {3},-1)$.
(I) If $\overrightarrow{a}$ is parallel to $\overrightarrow{b}$, find the value of $\sin ^{2}x-6\cos ^{2}x$;
(II) If $f(x)= \overrightarrow{a} \cdot \overrightarrow{b}$, find the interval(s) where the function $f(2x)$ is monotonically decreasing.

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