
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 $f(x)= \sqrt {3}\sin (2x- \frac {\pi}{3})-2\sin (x- \frac {\pi}{4})\sin (x+ \frac {\pi}{4})$.  
$(1)$ Find the smallest positive period of the function $f(x)$ and the equation of the axis of symmetry for the graph;  
$(2)$ Find the maximum and minimum values of the function $f(x)$ in the interval $\left[- \frac {\pi}{12}, \frac {\pi}{2}\right]$.

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