
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 $$f(x)= \begin{vmatrix} 2\sin x & \sqrt {3}(\sin x-\cos x) \\ \sin x+\cos x & \cos x\end{vmatrix}$$;  
(1) Find the smallest positive period of the function $f(x)$;  
(2) Find the range of the function $$y=f\left(x- \frac {\pi }{2}\right)$$, where $$x\in \left[0, \frac {\pi }{2}\right]$$.

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