
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 $f(x)=\sin (2x+ \frac {\pi}{6})+ \frac {3}{2},x\in\mathbb{R}$.  
$(1)$ Find the smallest positive period and the intervals of monotonic increase for the function $f(x)$;  
$(2)$ How can the graph of the function $f(x)$ be obtained by transforming the graph of the function $y=\sin 2x(x\in\mathbb{R})$?

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