
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 $f(x)=2\sin^{2}x+2\sqrt{3}\sin x\cdot\sin\left(x+\dfrac{\pi}{2}\right)$,
$(1)$ Find the minimal positive period of $f(x)$;
$(2)$ If the graph of the function $y=f(x)$ is translated to the left by $\dfrac{\pi}{6}$ units and then upwards by $2$ units, to obtain the graph of function $g(x)$, find the range of values of $g(x)$ in the interval $\left[0, \dfrac{7\pi}{12}\right]$.

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