
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 $\overrightarrow{a}=(1,\sin x)$, $\overrightarrow{b}=(\sin x,-1)$, $\overrightarrow{c}=(1,\cos x)$, where $x\in(0,\pi)$.  
(Ⅰ) If $(\overrightarrow{a}+ \overrightarrow{b})\nparallel \overrightarrow{c}$, find $x$;  
(Ⅱ) In $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $B$ is the $x$ found in (Ⅰ), $2\sin^2B+2\sin^2C-2\sin^2A=\sin B\sin C$, find the value of $\sin \left(C- \frac{\pi}{3}\right)$.

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