
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
If the function $f(x)= \sqrt {5}\sin (2x+\phi),0 < \phi < \pi$ satisfies $f\left( \frac {\pi}{3}-x\right)=f\left( \frac {\pi}{3}+x\right)$ for any $x$.  
$(1)$ Find the value of $\phi$;  
$(2)$ If $x\in\left[- \frac {\pi}{12}, \frac {\pi}{2}\right]$, find the maximum and minimum values of $f(x)$ and their corresponding $x$ values.

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