
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 $f(x)=\cos x(\sin x- \sqrt {3}\cos x)(x\in R)$
(I) Find the maximum value of the function $f(x)$ and the set of values of $x$ when the function reaches its maximum;
(II) In $\triangle ABC$, the sides opposite to angles $A$, $B$, $C$ are $a$, $b$, $c$ respectively. Angle $A$ satisfies $f( \frac {A}{2})=- \frac { \sqrt {3}}{2}$, $a=3$, $b+c=2 \sqrt {3}$, find the area of $\triangle ABC$.

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