
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 $f(x)=\sin ^{2}x+ \sqrt {3}\sin x\cos x+ \frac {2}{3}$, where $x\in\mathbb{R}$,
(I) Find the smallest positive period $T$ of the function $f(x)$ and the interval where it is monotonically decreasing in $\[-π,π\]$;
(II) If the equation $f(x)+k=0$ has exactly one real solution in the interval $\[0, \frac {π}{2}\]$, find the range of the real number $k$.

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