
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 $f(x)=\sin (2x+ \frac {\pi}{3})$.  
$(1)$ If $x\in(- \frac {\pi}{6},0]$, find the minimum value of $4f(x)+ \frac {1}{f(x)}$ and determine the value of $x$ at this point;  
$(2)$ If $(a\in(- \frac {\pi}{2},0),f( \frac {a}{2}+ \frac {\pi}{3})= \frac { \sqrt {5}}{5})$, find the value of $f(a)$.

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