
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 $f(x)=\cos (2x+ \frac {2π}{3})+2\cos ^{2}x$, $x\in R$.
(I) Find the smallest positive period and the monotonically decreasing interval of the function $f(x)$;
(II) After shifting the graph of the function $f(x)$ to the right by $\frac {π}{3}$ units, we obtain the graph of the function $g(x)$. Find the minimum value of the function $g(x)$ on the interval $[0, \frac {π}{2}]$.

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