
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 $f(x)=2\sin (2x+ \frac{π}{6}) + \frac{3}{2}$, where $x\in R$.

(1) Find the smallest positive period of the function $f(x)$;

(2) Find the interval(s) where the function $f(x)$ is monotonically decreasing;

(3) How can the graph of function $f(x)$ be obtained through transformations of the graph of the function $y=\sin x$ ($x\in R$)?

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