
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 a point P at coordinates $(\cos 2x + 1, 1)$ and a point Q at coordinates $(1, \sqrt{3} \sin 2x + 1)$, where $x \in \mathbb{R}$. If function $f(x) = \overrightarrow{OP} \cdot \overrightarrow{OQ}$ (with O representing the origin of the coordinates),  
(1) Find the explicit formula for function $f(x)$.  
(2) Determine the smallest positive period and the extreme values of $f(x)$.

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