
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 $\overrightarrow{a}=(\sin x,-\cos x)$ and $\overrightarrow{b}=(\cos x, \sqrt {3}\cos x)$, the function $f(x)= \overrightarrow{a}\cdot \overrightarrow{b}+ \frac { \sqrt {3}}{2}$  
$(1)$ Find the smallest positive period of $f(x)$;  
$(2)$ When $0\leqslant x\leqslant \frac {\pi}{2}$, find the range of the function $f(x)$.

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