
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 the function $f(x)=\sqrt{3}\sin x\cos x-{\cos }^2x$.  
$(1)$ Find the smallest positive period of $f(x)$;  

$(2)$ If $f(x)=-1$, find the value of $\cos \left(\dfrac{2\pi }{3}-2x\right)$.

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