
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 points $P(\cos 2x+1,1)$ and $Q(1, \sqrt {3}\sin 2x+1)$ (where $x\in\mathbb{R}$), and the function $f(x)= \overrightarrow{OP}\cdot \overrightarrow{OQ}$ (with $O$ being the origin),  
(1) Find the analytical expression of the function $f(x)$;  
(2) Determine the smallest positive period and the extremum values of the function $f(x)$.

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