
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 $f(x)=1+2 \sqrt{3}\sin x\cos x-2\sin ^{2}x$, where $x\in \mathbb{R}$.

(Ⅰ) Find the intervals of monotonic increase for the function $f(x)$;  
(Ⅱ) If the function $f(x)$ is translated to the right by $\dfrac{\pi}{6}$ units to obtain the function $g(x)$, find the minimum and maximum values of $g(x)$ in the interval $\left[- \dfrac{\pi}{2},0\right]$.

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