
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 $f(x)= \sqrt {3}\sin (x- \frac {\pi}{3})+2\cos ^{2} \frac {x}{2}$.  
(I) Find the interval of monotonic decrease for $f(x)$.  
(II) If the sides opposite to the internal angles $A$, $B$, $C$ of $\triangle ABC$ are $a$, $b$, $c$ respectively, and $f(A)= \frac {3}{2},a= \sqrt {3},\sin B=2\sin C$, find $c$.

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