
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 $f\left(x\right)=2{\sin }^{2}x+2\sqrt{3}\sin x\cdot \sin \left(x+\frac{π}{2}\right)$.

(1) Find the smallest positive period of $f\left(x\right)$;

(2) If the graph of the function $y=f\left(x\right)$ is moved to the left by $\frac{π}{6}$ units and then upward by 2 units to obtain the graph of function $g\left(x\right)$, find the range of function $g\left(x\right)$ on the interval $\left[0,\frac{7π}{12}\right]$.

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