
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 $f(x)=\sin (2x+ \frac {\pi}{6})+\sin (2x- \frac {\pi}{6})+\cos 2x+a$ ($a\in\mathbb{R}$, $a$ is a constant).

(I) Find the smallest positive period of the function;

(II) Find the intervals where the function is monotonically decreasing;

(III) If $x\in[0, \frac {\pi}{2}]$ and the minimum value of $f(x)$ is $-2$, find the value of $a$.

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