
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 that $O$ is the coordinate origin, $\overrightarrow{OA}=(2\cos ^{2}x,1)$, and $\overrightarrow{OB}=(1, \sqrt {3}\sin 2x+a)(x\in\mathbb{R},a\in\mathbb{R},a$ is a constant$)$, if $f(x)= \overrightarrow{OA}\cdot \overrightarrow{OB}$:
(1) Find the smallest positive period and the monotonically decreasing interval of the function $f(x)$;
(2) If the minimum value of the function $f(x)$ when $x\in[0, \dfrac {\pi}{2}]$ is $2$, find the value of $a$.

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