
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 point P(cos2x+1, 1) and point Q(1, $\sqrt {3}$sin2x+1), where x belongs to the set of real numbers, O is the coordinate origin, and the function f(x) = $\overrightarrow {OP}$ • $\overrightarrow {OQ}$.

(1) Find the analytical expression of function f(x) and its smallest positive period.
(2) Find the interval where function f(x) is monotonically increasing.

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