
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: $f(x)=2\sin (2x+ \frac {\pi}{6})+a+1$ ($a\in\mathbb{R}$, $a$ is a constant).

(1) If $x\in\mathbb{R}$, find the smallest positive period of $f(x)$;

(2) If the sum of the maximum and minimum values of $f(x)$ in the interval $\left[- \frac {\pi}{6}, \frac {\pi}{6}\right]$ is $3$, find the value of $a$;

(3) Under the condition of (2), find the intervals where $f(x)$ is decreasing.

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