
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 $f(x)=\cos x(\sin x- \sqrt {3}\cos x)+ \frac { \sqrt {3}}{2}$, where $x\in\mathbb{R}$.
- (I) Find the smallest positive period of $f(x)$ and the intervals of monotonic increase;
- (II) If the function $g(x)=f(x+a)$ is even, find the minimum value of $|a|$.

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