
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 $$f(x)=\cos(2x+ \frac {2\pi}{3})+2\cos^{2}x$$,  
(1) Find the smallest positive period of the function $f(x)$ and its intervals of monotonic decrease;  
(2) After shifting the graph of the function $f(x)$ to the right by $$\frac {\pi}{3}$$ units, we obtain the graph of the function $g(x)$. Find the minimum value of the function $g(x)$ in the interval \[0, $$\frac {\pi}{2}$$\].

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