
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 $\overrightarrow{m}=({2sin({x+\frac{π}{6}}),1})$ and $\overrightarrow{n}=(2cosx,-1)$.<br/>$(Ⅰ)$ If $\overrightarrow{m}∥\overrightarrow{n}$ and $x\in \left[0,\pi \right]$, find the value of $x$;<br/>$(Ⅱ)$ Let $f(x)=\overrightarrow{m}•\overrightarrow{n}$, find the monotonic interval of the function $f\left(x\right)$.

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