
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 $f(x)=4\cos \left(x- \frac {\pi}{2}\right)\cdot \sin \left(x- \frac {\pi}{3}\right)-1$.  
$(1)$ Find the smallest positive period of the function $y=f(x)$.  
$(2)$ Given in $\triangle ABC$, the sides opposite angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively, and $a$, $b$, $c$ form a geometric sequence, find the range of $f(B)$.

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