
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
Let the function $f(x)= \sqrt {3}\sin x\cos x+\cos ^{2}x+a$  
$(1)$ Write down the smallest positive period of the function $f(x)$ and the interval where it is monotonically decreasing;  
$(2)$ When $x\in\left[- \dfrac {\pi}{6}, \dfrac {\pi}{3}\right]$, the sum of the maximum and minimum values of the function $f(x)$ is $\dfrac {3}{2}$. Find the solution set for the inequality $f(x) > 1$.

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